Is she capable in combat or a slouch because raul is a killer man! Hope its not going to be a big drop off. Also will raul go to his shack when I dismiss him just in case I try to find him again?

Veronica Punches things. They die when she punches them. Give her a ballistic fist, and they will explode and die when she punches them.
That's all you really need to know.
Oh, and if you ever come across a Q-35 Matter Modulator, she's pretty handy with that too.

Will she use a gun or melee weapon? Where can I get a ballistic fist? Does raul go to his shack?

Well, she doesn't really need a melee weapon, she does good enough with her default powerfist.
You can get a ballistic fist at the Brotherhood of steel bunker. If you take her to the Followers, the NCR, and the Silver Rush, and other places where non BOS have tech, and she'll get you into the BOS bunker. You can buy all sorts of good stuff there, and when you do their quests you can get even more good stuff.

She'll use a 10mm pistol if you make her, but I haven't been able to get her to use any other gun besides the unique Plasma rifle.

When you get her she uses a Power Fist. She's OK, pretty decent. She can use guns and melee weapons. Raul goes where you tell him to go for example, The Lucky 38 assuming you have the presidential suite unlocked or where they were living where you found them. Btw just a side note, if you want to be literally unstoppable get Boone over in Novac. He's able to get head shots from very far range, finds the enemies usually before you can, and is pretty sick with a melee weapon. Bromance?

Is veronica's quest "I could make you care" because for some reason that quest unlocked for me when I got c-finder. If that's not the quest qho do I have to talk to specifically and what's the reward for completing her questline?

And I do not have the lucky 38 suite I haven't talked to house yet. I do have the tops suite though got it after talking to benny.

Yeah, that's the one.
It either upgrades her armor rating or her unarmed attacks.

I hope the quest isn't bugged because I haven't talked to her yet but it unlocked for acquiring c-finder for some reason.

I put her in a set of power armor as well, and once you do her quest she gets a perk that increase her DT more. She is a great tank and do good damage too. I've only used her and Cass and I like veronica more.

Will I get power armor from her?

She seems to be bugged. Her hit point stays at 215 regardless of my level and her damage threshold stays the same no matter what armor I give her.

Yea Her HP dosent move.And I havent noticed how to check her damage threshhold...how does one do that?

You need the Living Anatomy perk. Once you get it, you get to see the health and DT of anyone you target in VATS. The DT is adjusted for your weapons and your perks so if you have armor piercing ammo or a perk that lets you bypass DT then the DT will show up as being lower than it really is.

Veronica has a fixed level of 12 and does not progress with the Courier unlike the other companions (her and ED-E are the rare exceptions).
I prefer her over Boone since I'm the one that usually does headshots from ridiculous range thanks to ED-E, and I need a tanker.

http://www.newvegasnexus.com/imageshare/images/263027-1287894676.jpg -> Personal mod, mind you.