Yes. First of all, if you want your buddy to be able to keep his save file on your system, the first thing you have to do is make a Mii on your WiiU and make it an account. Open up MH3U on the WiiU, have him make his file, and then use the data transfer tool to move it to the 3DS. From that moment, he can always transfer the data back to his side of the WiiU so that you can use the 3DS with your file if you ever want to.
Now down to playing online. Go to an online room, and then talk to the old geezer in the middle, and tell him that you want to post a request. It will open the "room Options" again, and the lady behind him will ring the Gong. The moment she does this, your friend goes to "multiplayer" and searches for a room. That room will show up, and he can join. At this point, you are now both online and playing. 2 more people can join you guys, and you can continue playing.
He can't leave the room or he will be disconnected.