Civilization – Are the diplomacy actions (trade etc) only available from the leader meeting screen

Unfortunately, it's not possible to cancel an Open Borders agreement. You just have to wait for whatever turns remain for it to expire.

Or you can go to war with them, which "kind of" cancels it :)

I'm currently playing my first successful game on immortal. The most important thing to keep the AI from attacking you is to have a strong enough military that you aren't an easy target. This means that you might have to forego wonders and other early buildings to catch up to the AIs starting units. You should also focus on scouting early, so you can meet as many city-states as possible, find some ruins, and kill some barbarians, all of which boost your economy. In my experience, it also means that you're going to have to attack someone early on in order to catch up to everyone else's growth. A few good puppet cities (preferably with one of those wonders you skipped) will put you back on par with the other AIs.

Some other tips regarding relations I've learned

• Try to get a pact of cooperation early on, while there's still plenty of space between you and the other civ. They aren't time limited, so it can help protect you for a long time.
• I've been turning down pact of secrecy offers, they limit my ability to be friends with as many people as possible.
• I've also been turning down open borders, this just allows the AI to scout me and see that he likely has a military advantage.
• I didn't settle many cities (only one in fact, the rest of my cities were captured). Eventually the AI settled near me, and this did cause our relations to sour, but at least it put it off.
• I've never given money to other civs, but I have occasionally given them free resources if they ask for them nicely.
• Research agreements are good, but be careful that you don't help one AI get too big of an advantage. I try to make agreements with the civs that have a lower score.