"If your right hand is causing you pain,
cut it off, cut it off" means that if the one closest to you causes you pain and sorrow, you should seperate yourself from him/her. And the next part of the verse is probably that you shouldn't have to try to keep your friends close, they will always be there if they are true friends, so the ones who's letting go is not worth you.
The lightning in the room, they sing about, is probably the tension between them, and they know they have to talk about it, but they try not to, that's why he says he's not a talker. To avoid the conversation that will end it.
Then they go on with their longing for an adventure. I think its because they need to get away for a while and do something together that will make them forget their problems(him-and-the-loved-girl) That way they will find back to their old love.
And yeah, they both want to stay together but they have alot of problems they need to talk over:-))