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You want to wait until right after it blooms to prune. Pruning now will cut away some of the growth that the blooms will flower on, which means that there will be fewer flowers.

It is highly unlikely that the lilac will cause damage to a foundation. They have very non-aggressive root systems and this is why you often see them used as foundation plants. The only way that it could be a threat (and even then, the plant would probably die before it did damage) would be if the roots were restricted tightly, as in there were only a few feet for the roots to grow in. That does not sound like the case where you are, so the lilac is not a threat.

Pruning them in early spring will not hurt the plant, but it will greatly reduce the amount of blooms you get this year. If this is not a concern, you can prune in early spring. Otherwise, wait until right after they bloom to prune them.

It has powdery mildew. These articles will help:
https://www.gardeningknowhow.com/problems/get-the-cure-for-powdery-mildew.htm
https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm

If you can transplant at any time, spring and early fall are the best times. To reduce shock, trimming may help. Dpending on its size, you can cut it back by 1/3 to help it recover from the move better, but if you remove all of the branches, the plant will take several years to bloom.

This article will help when you transplant it:
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

For the most part, they are deer resistant. That being said, no matter what the plant, if a deer is very hungry, it will eat almost anything. This is why they say deer resistant rather than deer proof.

Here is a link with a list of deer resistant plants:
https://www.gardeningknowhow.com/plant-problems/pests/deer/deer-resistant-plants.htm