We know that the DA began to limit its activities after losing Luna at Christmas and Ginny at Easter, and eventually most of the members ended up in the RoR, starting with Neville. But do we know whether Neville started hiding out in the RoR only after Ginny didn't return from the Easter holidays? Or could he have already been "missing" before she left, sneaking out at night to do DA business, and simply found it too hard to continue once Ginny was gone? I'm trying to get a timeline of what happened at Hogwarts between Christmas and Easter straight in my head, particularly involving Neville.
All I remember is that it was after Dawlish (I think) was sent to capture his Gran. I think it was after Ginny went but as I don't have my copy of DH handy I am not entirely sure.

How would Neville act romaticly?
Hmm this is a good one. As we don't see him acting romantically in any of the books (unless there's anything mentioned in GoF about the Yule Ball) I think you can portray him how you like, but keep in mind that this is in 7th year so he is quite confident and he knows Luna very well.

What sort of things did Luna and Neville do together to overthrow the carrows?
Well we know the DA put graffiti around the castle saying things like "Dumbledore's Army, still recruiting." and things like that but they also rescued first years from the dungeons and stood up to the Carrows in class (i.e by refusing to use the crutiatus curse, Neville asked the muggle studies teacher how much blood she and her brother have.). Neville, Ginny and Luna were the leaders so they would be trying to cause the most trouble and don't forget the three of them tried to steal the sword of Gryffindor from Snapes office.

Hope I've been of some help,

~Abi~