can i plant annual planters in just compost and peat moss?:

In theory, no. Commercially sold compost has been produced with heat, which sterilises any diseases and weed seeds so that they can't grow. Unless your own compost was produced within 3 months by being regularly turned and covered (i.e., hot composting) it won't be sterile. But some people just risk it anyway.

Your own compost and peat moss are OK, but do add some grit if you buy in plants, the compost in which they are grown should give them a start. After a few weeks liquid feed. Although you are across the pond, it should not be any different than here in England.

The manure should have been allowed to rot for at least a year before use. Use it sparingly as a feed in the compost mixture, strong fertiliser can scorch roots.