Since you are out of status for more than a year you are in jeopardy of a 10-year ban if you get caught. Or if you leave the country.
1. you can marry your girlfriend anywhere you want. I would suggest you do it here.
2. Sure, but when you leave the US, since you haven't adjusted status here you will have effectively overstayed your visitors visa and will be banned. Since you overstayed for over a year you will be slapped with a 10-year ban as soon as you leave the country. So NO, it is not possible given your situation/scenario. The ban can be waived if you marry a USC, but it's another complication in the process and will cause delays and will ultimately affect your relationship with your wife. I would say this is NOT an option in my opinion.
What I would *suggest* (this is NOT legal advise, always take what you get here and pass it by an attorney if possible) is to get married here in the US - RIGHT AWAY. If you get deported you have another hurdle in front of you + a 10 year ban.
Then submit an AoS (adjustment of status) with your wife to get you legitimized in this country. You can file for an AP (advanced parole) to then let you leave/travel from the country to wherever you want to go for a specified amount of time. These aren't always given though, so plan accordingly.
To file the AoS you and your fiance/wife will need to fill out the following forms:
I-130
I-485
I-864
I-765 (optional but recommended)
I-131 (optional but recommended)
Be sure to follow the instructions for each form and be sure to provide as much backing evidence to your case as possible!!! You will also need to have a medical exam by a USCIS approved medical practice. Always check the USCIS website/forms for updated filing fees as well. If you send in the incorrect fee amounts they may return/reject your AoS (you can always file again, but it's delayed) Check out the book in my signature if you would like a cheap but awesome do it yourself aid... use it in conjunction with this forum and you'll be golden. There are many here who have real-life experience in this area and can provide invaluable advice. All this combined with an attorney and your chances of success increase dramatically! Good luck, I hope eerything works out for you - be sure to post here for more help!
DO NOT LEAVE THE COUNTRY UNTIL YOU HAVE APPLIED FOR AOS AND RECEIVED YOUR AP OR UNTIL YOU HAVE RECEIVED YOUR GREEN CARD. You will cause yourself massive amounts of headache.... With that said, good luck
