I can't even find the, "Hey, let's stop fighting" option....

Then the ai breaks it the next turn. There ought to be some minimum time delay before being able to declare war again, or, at least a heavy diplomatic penalty with all the other races for breaking a peace treaty too soon.

I never did like the time limits on treaties in Civ 5.

It either creates the micromanagement of periodically renewing them, or the artificiality of the impossibility of a treaty backstab.

I'd rather the AI just generally be more likely to honor treaties with parties it otherwise has good relations with. Or create a 'cease fire' treaty that is a prerequisite to the peace treaty, that is easier to break.

I want an easy way to see who has which ideology, and who is at war with whom. I am sure this will come some day, but sooner would be better than later.

I too would really like to see the things that the OP mentions as well as an easy way to find out who is at war with who, I might want to influence things!  The same goes for being influenced, a sign of a good ai when it comes to diplomacy is thinking about these kinds of things & quietly propping up the cat's paws you use to poke your enemies in the eye with rather than always doing ityourself, that goes double for helping your useful allies if they are threatened in the wrong ways & pulling their leashes if they get a bit too uppity towards the wrong folks.... granted that last bit might be too much for now, but putting a thumb of a scale when you have an interest in in fight is different.