Cutting out the infected branches is a great starting point. I'd not wait to spring, however, for some of them --- that's when the fungus releases its spores and can reinfect the plant. Winter is a better time to cut out all of the affected wood. Also, when you prune out the fungus, cut the branches at least 8 inches back from where you first see the knot. Throw the pruned off bits in the trash. I'm not sure what fungicides are labeled for use on black knot in your area, but you might also look at spraying your tree from spring to early summer.
As far as the second problem on the tree goes... Without seeing it, I can't really give specific advice for you. You might have a local arborist come out and take a look --- after examining it in person, they'll be able to give you a better answer.
---Justin, Senior Garden Editor, BHG.com