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Anytime between now and the end of March will be fine for pruning these trees.

It depends on the variety. There are some new varieties that will grow in Zone 6. The ones we have seen like this, however, never really take on a tree form, but rather stay bush like as they die back to the ground each winter.

You don't normally need to fertilize them, but a little fertilizer a bit higher in phosphorus once every year or two is helpful.

These articles will help you:
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/pruning-crepe-myrtle-trees.htm
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/best-crepe-myrtle-pruning-time-when-to-prune-crepe-myrtle.htm

There are a number of reasons that may cause crepe myrtle's failure to bloom. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-not-blooming.htm

You can trim off the blooms right after they fade. As a matter of fact, trimming them right after they fade may result in a second batch of blooms.