Confused about A Scandal in Bohemia

Why did Irene get married on such short notice? Why couldn't they have gotten married in the morning? It wasn't a coincidence that they just so happened to get married that day, was it?

Why did Irene give up? If it was because of Holmes finding the location of her picture, couldn't she just have moved it?

Was it really necessary to flee the country instead of just giving up the picture? The king could have solved the problem by killing her, but he didn't, so was she really in danger?

Seriously, what the hell.