I've played BTS for several games. I notice some wired stuff that I can't explain.
1, It shows ' peace treaty (10 turns) canceled by XXX(leader)' , but there is no war indicated in the foreign advisor screen.
2, part of trade agreements cancelled by several leaders altogether. I think it might be the effect of the AP wonder. but I can re-negotiate them immediately after that.

1, It shows ' peace treaty (10 turns) canceled by XXX(leader)'

This simply means, that either of you can now declare war.

1. You can cancel a peace treaty without having war. Peace treaty means you cannot have war at all with them. No treaty is just neutral.

Peace treaties are automatically applied between two parties after a demand is given and accepted. This prevents the player and the AI from attacking one another if they've just made an appeasement. For example, if an AI demands a technology and you give it to him, war cannot begin between you for ten turns. Similarly, if you demand a technology and the AI gives it to you, war cannot begin between you for ten turns.

Peace treaties are automatically applied between two parties after a demand is given and accepted.

Yep, that's right. I found this out in my first game by applying my usual tactic of demanding all the cash from the AI just before I declared war (stopping them upgrading troops). They gave in and then I found I couldn't declare. :mad:

Its a good change I think.

Yes, if many people stop trading with you at once, it is due to the Apostolic palace. You might be able to renegotiate trade deals, but iirc AI won't accept open borders for some turn after it is canceled.