Mulberry: Cherries don't get fire blight so no concern there. It might be better planted 10ft away or at least a few feet. But for us backyard growers other considerations usually prevail. So I'd say plant it wherever is best for sun etc. Do remove all of the apple stump that you can if it's rotted. But again I won't spend $$$ removing a solid stump.

dmc, You're in the heart of fireblight country. Some varieties are exquisitely sensitive, others are tolerant - take a lickin' and keep on tickin' - but none, that I'm aware of are totally resistant to it. I've lost a few apples/pears/quince to FB through the years, but if they can't make it under my (lack of) management scheme, they don't belong here anyway. I try to prune out FB strikes whenever possible, but I've got a bunch of blackened shoots in several pears out in my orchard right now that I've just not gotten around to cutting out, and I'm not fretting over 'em. They look to have progressed as far as they're going to this season. I will prune 'em out at some point, if only to diminish the potential for them to act as a source of new infection next year. Stay tuned for opinions/recommendations from orchardists who have a more hands-on approach.

Fire Blight enters the plant from blossoms or wounds and the bacteria can be transferred on pruning tools. The symptoms you describe could certainly be caused by this bacteria. Here is a link to information from the University of California at Davis which gives symptoms and treatment options. Here is a link that might be useful: Fire Blight

Here in SoCal, the apple blossoms have been or already are in full bloom so it's actually a bad time to prune. Bad timing is still better than no pruning at all though. If your spring weather hasn't started, you may have some time left with which to prune. I'm not an expert on the disease by any means, having only dealt with it once. I participated in a class put on by Dave Wilson nursery, a Ca. fruit tree grower. In the class, there were several apple trees with apple blight shoot strikes. We pruned the material and made sure to disinfect the pruners with a bleach water solution to keep from contaminating other trees.