When you say, "Anybody set to break siege will fight in the same battle as anybody moving in from an outside province."
will this battle take place outside the castle in open land, or will the defenders somehow sneak past me, and defend from within the castle?
The battle takes place outside the castle. The guys breaking siege all run outside and join whatever friendly forces are moving into the province that turn.
Merry look up the section in the manual on how the turns are resolved. It will show you the order of events which happen every turn and give you a clear guide to all further questions about ordering.
To just run it down quickly in terms of combat, you'd have:
Magic Combat (teleports, remote summons, etc)
Assassinations
Regular Combat
Fort Storming