Janine, I'm going to answer several of your questions with a wrap up of Part I, The Window. I think this will complete my understanding of Mrs. Ramsey as a character.
First notice how Mrs. Ramsey is characterized in Lily's painting:
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Nothing could be cooler and quieter. Taking out a pen-knife, Mr Bankes tapped the canvas with the bone handle. What did she wish to indicate by the triangular purple shape, “just there”? he asked.
It was Mrs Ramsay reading to James, she said. She knew his objection— that no one could tell it for a human shape. But she had made no attempt at likeness, she said. For what reason had she introduced them then? he asked. Why indeed?—except that if there, in that corner, it was bright, here, in this, she felt the need of darkness. Simple, obvious, commonplace, as it was, Mr Bankes was interested. Mother and child then—objects of universal veneration, and in this case the mother was famous for her beauty—might be reduced, he pondered, to a purple shadow without irreverence.
A purple triangle, symbolizing power, strength, and as mother and child, a modonna with child.
And then a couple of chapters later, when Mrs. Ramsey is in her stream of conscious contemplation, she conceives of herself:
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No, she thought, putting together some of the pictures he had cut out— a refrigerator, a mowing machine, a gentleman in evening dress— children never forget. For this reason, it was so important what one said, and what one did, and it was a relief when they went to bed. For now she need not think about anybody. She could be herself, by herself. And that was what now she often felt the need of—to think; well, not even to think. To be silent; to be alone. All the being and the doing, expansive, glittering, vocal, evaporated; and one shrunk, with a sense of solemnity, to being oneself, a wedge-shaped core of darkness, something invisible to others. Although she continued to knit, and sat upright, it was thus that she felt herself; and this self having shed its attachments was free for the strangest adventures. When life sank down for a moment, the range of experience seemed limitless. And to everybody there was always this sense of unlimited resources, she supposed; one after another, she, Lily, Augustus Carmichael, must feel, our apparitions, the things you know us by, are simply childish. Beneath it is all dark, it is all spreading, it is unfathomably deep; but now and again we rise to the surface and that is what you see us by. Her horizon seemed to her limitless. There were all the places she had not seen; the Indian plains; she felt herself pushing aside the thick leather curtain of a church in Rome. saw it. They could not stop it, she thought, exulting. There was freedom, there was peace, there was, most welcome of all, a summoning together, a resting on a platform of stability. Not as oneself did one find rest ever, in her experience (she accomplished here something dexterous with her needles) but as a wedge of darkness.
She concieves of hersef as a wedge of darkness, which connects to Lily's purple triangle. But then she identifies with the lighthouse light:
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Losing personality, one lost the fret, the hurry, the stir; and there rose to her lips always some exclamation of triumph over life when things came together in this peace, this rest, this eternity; and pausing there she looked out to meet that stroke of the Lighthouse, the long steady stroke, the last of the three, which was her stroke, for watching them in this mood always at this hour one could not help attaching oneself to one thing especially of the things one saw; and this thing, the long steady stroke, was her stroke. Often she found herself sitting and looking, sitting and looking, with her work in her hands until she became the thing she looked at—that light, for example.
She identifies with the third stroke, "her stroke." Triangle, wedge, third stroke, all based on the number three. What does the number three signify? Let's return to Lily's painting where Lily is pondering the form after Mr. Bankes has questioned her:
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She could not show him what she wished to make of it, could not see it even herself, without a brush in her hand. She took up once more her old painting position with the dim eyes and the absent-minded manner, subduing all her impressions as a woman to something much more general; becoming once more under the power of that vision which she had seen clearly once and must now grope for among hedges and houses and mothers and children—her picture. It was a question, she remembered, how to connect this mass on the right hand with that on the left. She might do it by bringing the line of the branch across so; or break the vacancy in the foreground by an object (James perhaps) so. But the danger was that by doing that the unity of the whole might be broken. She stopped; she did not want to bore him; she took the canvas lightly off the easel.
"It was a question [of] how to connect the mass on the right hand with that on the left hand." To connect one with two requires three, the completion of a triangle, the third stroke. Mrs. Ramsey is the connecting foil, bringing isolated people together. You know this is the most curious stream-of-conscious novel I have ever come across. Most stream of conscious novels maintain one person's stream of conscious for either a extended length or at least a chapter. Woolf not only crosses from one person's stream of conscious to another from paragraph to paragraph, but she often crosses from one person's consciousness to another's in the very same paragraph. This is not by accident, it is aesthetically representing something. The isolation of the interior mind crosses and touches other people through a special person, a person who brings people together, tries to arrange marriages, invites guests to her home, and through a dinner party (a last supper, perhaps?) unites individuals to a community. Notice this at the beginning of the dinner party:
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Raising her [Mrs. Ramsey] eyebrows at the discrepancy—that was what she was thinking, this was what she was doing—ladling out soup—she felt, more and more strongly, outside that eddy; or as if a shade had fallen, and, robbed of colour, she saw things truly. The room (she looked round it) was very shabby. There was no beauty anywhere. She forebore to look at Mr Tansley. Nothing seemed to have merged. They all sat separate. And the whole of the effort of merging and flowing and creating rested on her. Again she felt, as a fact without hostility, the sterility of men, for if she did not do it nobody would do it, and so, giving herself a little shake that one gives a watch that has stopped, the old familiar pulse began beating, as the watch begins ticking—one, two, three, one, two, three. And so on and so on, she repeated, listening to it, sheltering and fostering the still feeble pulse as one might guard a weak flame with a news-paper. And so then, she concluded, addressing herself by bending silently in his direction to William Bankes—poor man! who had no wife, and no children and dined alone in lodgings except for tonight; and in pity for him, life being now strong enough to bear her on again, she began all this business, as a sailor not without weariness sees the wind fill his sail and yet hardly wants to be off again and thinks how, had the ship sunk, he would have whirled round and round and found rest on the floor of the sea.
"Nothing seemed to have merged. They all sat separate. And the whole of the effort of merging and flowing and creating rested on her." She brings them together. She feels each guests (Tansley's impoverished upbringing, Bankes's family loss) isolating pain, "for if she did not do it nobody would do it, and so, giving herself a little shake that one gives a watch that has stopped, the old familiar pulse began beating, as the watch begins ticking—one, two, three, one, two, three. " One, two, three! The third connecting stroke, completing the triangle. Notice later when she lights the candles:
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Now eight candles were stood down the table, and after the first stoop the flames stood upright and drew with them into visibility the long table entire, and in the middle a yellow and purple dish of fruit. What had she done with it, Mrs Ramsay wondered, for Rose’s arrangement of the grapes and pears, of the horny pink-lined shell, of the bananas, made her think of a trophy fetched from the bottom of the sea, of Neptune’s banquet, of the bunch that hangs with vine leaves over the shoulder of Bacchus (in some picture), among the leopard skins and the torches lolloping red and gold... Thus brought up suddenly into the light it seemed possessed of great size and depth, was like a world in which one could take one’s staff and climb hills, she thought, and go down into valleys, and to her pleasure (for it brought them into sympathy momentarily) she saw that Augustus too feasted his eyes on the same plate of fruit, plunged in, broke off a bloom there, a tassel here, and returned, after feasting, to his hive. That was his way of looking, different from hers. But looking together united them.
and a little further down:
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Some change at once went through them all, as if this had really happened, and they were all conscious of making a party together in a hollow, on an island; had their common cause against that fluidity out there.
Mrs. Ramsey unites their individual isolations against the "fluidity out there," the natural forces bent on human destruction. It all pulls together, the isolation, the uniting into a community, the fight against life's darker forces.