If I remember correctly when you declare a truce the ships that they had in your territory are free to exit your territory in any fashion they choose, which means they can meander about a bit before doing so. However they should not be able to enter your territory without either war, stealth, or open borders. They are free to go to outposts which you own but are not in your territory. Also anyone (including you) is free to visit any system that they don't know is owned because they've never seen it, even if it's obvious. This can be exploited to put a ship into enemy territory then "leave" into "unknown" territory (that you know they obviously own), and explore their space. That's not a bug so much as abuse of intergalactic law. Are they AI entering your territory after the truce, or just not leaving as fast as you'd like?

As far as peace demands that isn't a bug per se, just them being rude. They want to take as much as they can get and they take other things into consideration such as if you are in another war. They know if you're in another war you might accept what would otherwise be a bad deal to get out so you can focus your ships. If you really are winning the war then just beat them up some more and they will eventually give you a good deal. They might think you aren't doing as well as you are because you have low invasion power, low industry relative to them, or some other factor that makes them think they can make a comeback.

Then you are in luck, in Endless Space 2 you can act just that. The way "religious" aspect of diplomacy works, is that burden of formal war declaration (and spending influence) lies on non-religious factions.