Them touching each other won't hurt the trees.

What's wrong with the limbs touching?

it appears that cooties are a potential concern for the poster ... lol ...

your best suggestions will come with a couple pictures ...

ken

ps: you know.. a while back .. it was all the rage.. to plant two different flower color shrubs/plants close together.. so they would grow together and have a fancy two tone flower show.. presuming they bloomed at the exact same moment in time ... or a clematis in another shrub ... two season flowers ...[and of course.. i cant come up with a search term to find examples of such ...]

Yes please, now's the time to prune! Definitely thin out the lower branches. Pics would help with specifics, but here's a good guide to trimming.

https://www.finegardening.com/article/pruning-crape-myrtles