Ironically, I think having a Twitter clone be called Open-X might fly legally, since that's generic enough, but pretty much any other instance where the trademarked name is very specific, like Open-Google or Open-Facebook would be surely easy to be removed by a judge. It's just that it takes a while for this process to happen, and until there's a legal injunction you can still use the name.

I bet that this will result in a letter from a lawyer, if this gets any traction.

Depends on how rich and powerful you are.

Usually, no. If they have a registered trademark, you definitely can't.