Actually, it's hard to murder a crepe myrtle once it's gotten established; homicide usually requires the use of a spade.

Now: a) Crepe [or crape] myrtles bloom on new wood. A certain amount of pruning reminds the plant to make new growth - which should give you new blooms the following season. Because CM is a summer bloomer, the general practice is to prune right after blooming is finished, otherwise you're cutting off the next season's flowers.

b) No one really agrees on how or how much to prune. It mostly depends on what you like plus what the CM plans to do. You can encourage a tree shape by keeping side branches pruned, or encourage a bushy shrub by severe pruning.

c) Weak branches: It sounds as though the roots might have been pruned when the screen porch was built. The CM should have accommodated by now, but it's possible there is too much top growing for the smaller root area. It's also possible that it isn't getting as much sun -- does the porch shade it now when before it was getting sun? Also, it's very likely that if you are in an area suffering from drought, that the plant simply is not getting enough water to support the branches. OTOH, CM branches are rather flexible, so if the branches aren't breaking from the weight of wet blooms, don't worry about them unless a broken branch could cause damage to the house.

Here is a link that might be useful: Pruning crepe myrtles