1. 10' is too far to function as a vent for this, you need one closer.
2. Hard to say...
3. If the shower is vented, trapped, and you have the proper slope, no, unless the line gets clogged.
If the stack is draining things from upstairs, you can't (or at least shouldn't) run your vent into it unless you do it above the flood plane of the highest drain (i.e., probably in the attic would be easiest). You might find it easier to just run a new separate vent in a more convenient place.