Sure, but wait a while from when you cut them from the parent plant until you move them.

It is called layering when a branch touches the ground and forms new roots. However, the branch is now using both the original roots and the new roots. When the new roots are well enough established, the connection to the main plant is cut, but it takes a while for the layered branch to get acclimated to using just its own new roots. If you cut it now, I would wait until next spring or next fall to move. It is OK to move in spring, but you will need to monitor it in dry weather to see if it needs watering.

Here is a link that might be useful: How to grow rhododendrons and azaleas.

And as for the 'trimming' of your other azaleas and rhododendrons, it's a little late in the year for that.
The azaleas would probably send out new growth from dormant buds that would have time to harden off before cold weather, the rhododendrons may not have that time depending on the size/age of the branches you were cutting.

Flower buds for both are being set now, pruning would remove next Springs flowers. Better would be to wait until immediately after bloom in Spring.

Thank you I will wait for next spring.