Planetary Bombardment in Treaties

Yes, it applies to every race you know.

There's a name for agreeing not to bombard the specific race you have a treaty with. It's called peace.

Indeed. Silly humans need to learn how to play with the AI.

Default things that seem to be part of all treaties(these are all relative to the race you have the treaty with and NOT other races):
Diplomatic status slowly improves.
Cannot colonize systems that they have colonies in.
Cannot attack their planets.

Things NOT covered automatically by a treaty:

Intel, you can do anything you want. This will have diplomatic repercussions though.

Fleet combat, it has diplomatic consequences, but unless specifically stated otherwise your ships and theirs will fight each other. I've even seen one of my allies blow up one of my survey satellites and then turn around and ask me for military assitance in blowing up the rest of them. X(

And did you agree?

I did send ships to the system. apparently they'll quit shooting your sats if you have ships there.