Evatrio, welcome to the game and these forums 
I’d offer you a place in my group, but I’m in Dawn, not Wintermark. I suspect someone will try to recruit you soon, and if not, just head along to the Wintermark Facebook page. I would definately reccomend you find a group to join for your first larp, even if you don’t spend much time with them.
First: I can reccomend some form of light armour, even for a healer on the battlefield. Light armour = +2 hits, and that will keep you alive from a passing blow or two. I can visualise a Wintermark battle healer in ;eather vest, shoulderpads, bracers and helmet, possibly with some interesting decoration, over a dark shirt and trousers. With a large pouch on one hip, a sword on the other, and possibly a bandolier of bandages and potions as well.
Second: Yes a sword. Or an axe, or something. Fairly reasonably, the barbarians like trying to kill the healers. You may find yourself having to parry a blow or two, or being able to finish off that last orc, and that’s always useful. Heck, if you’re carrying a mace, you could even use it medically (“Hold still, I’m going to bash that shoulder back into place, this is going to hurt…”)…
Third: Hell yes. The Imperial Hospital (set up by PCs during the game) is a dull green tent with a banner (carrying the rune of blood, red on white) that sets up next to the Sentinel Gate every event. They heave triage stations, benches, supplies, experienced (IC and OOC) personel, and knowledge of every sort of horrible injury. An excellent place to learn the medic game.
Fourth: Tricky one this. Lets assume you’ve gone full healer, including apothecary and a herb garden resource. You can sell off a few herbs, make potions for other people for a small fee (especially if they’re supplying the herbs), but the actual patching up of folk is normally done for free. At the hospital, they have a donations basin, which funds their work. I’ve heard of League doctors who leave their business card in the bandages of patients (“If you have survived, it has been due to the work of Dr X, maybe you should buy them a drink next time you see them. Reccomend me to your friends!”). But as a rule, you don’t charge for saving the lives of people on the field of battle. Given that they have probably been fighting hard on the front lines, you could say they’ve paid in advance…
Or, to put it another way: Apothecary you can make some money from. Battlefield healer you can make some friends from.
Happy to discuss physreps and where to get them on request 