I would say to leave the peonies alone for now. Watch them daily and if the stems turn black then cut them off at ground level. You should get new sprouts, if not this year then next. Their root systems are pretty hardy and they can often live 70 years or more without being transplanted. There are tree peonies that are shrub like and have woody stems in the winter and herbaceous peonies that die down to the ground in the fall. Remove the spent foilage in fall when they start to look shabby.
You don't say where you live or your hardiness zone so I can't say for sure what is going on with your fruit trees. If you've had a hard frost it could kill the flower buds for this year.
Here's some helpful info on your lilacs.
Sounds like you have a lovely place!
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.