So sorry I didn't see your post sooner. Your hardy geranium wants to stay outside in the ground for the winter. It needs a dormant cold period and it's hardy in your zone.
Unless you have hardy begoinas, and not the houseplants, then you need to bring in the begonias for the winter. Do you know which begonia you have? Here's a site on begonias so you can id what you have and one for their care too.
Your mums should be fine outside. Just cut the dead stems in the spring.
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.