In order of your questions.
Give them a decent mech with some armor, or a flier. The +3 bonus to their defense roll due to being a flying unit will help them, especially if you can get a half decent MV for the mech. Oh, and don't give lancemates blast weapons.
Camaraderie is basically useless. There are always a few people willing to join up, and you can always choose to look for a lancemate in story missions.
Loot mostly. There aren't too many fliers out there, Skull, Wraith, and Shard are the most common, but don't give your lancemates the Shard since it has a blast weapon. Otherwise, just keep looking. I got a Coriache from a mission against pirates, and its an amazing hoverfighter. The skull is likewise an amazingly good hoverfighter, and it starts with a delightful turret.
Lancemates do indeed use any out of combat skills they start with. If they have repair and repair materials on them, they'll fix their own mech up after combat automatically, if they have first aid fuel and medicine they'll heal you automatically in dungeons, and if they have an activated skills, you can use them yourself. Unfortunately, 99% of the time, they only have the combat skills, since this was a change from GH1 to promote your pilot being the focus. I lucked out and my first lancemate got Jack of All Trades, so he has a massive number of skills and xp now. He's also far and away the most powerful in the group, even though his mecha skills are 4-5 points lower then my pilots and the other lancemate.