Didn't specify FW or RW. FW is pretty much covered above so I've give you the RW side of the house.
1) Yes it's possible to make a career out of air ambulance. We have pilots who retire 20 yrs military and then do this for another 20 yrs. We have Vietnam dudes still flying with us. Its a job that has young pilots from low 2,000 hrs to pilots with 15,000 + hrs.
2) Yep, home every night but they're 12 hrs days / nights. 7 on and 7 off so yes, you're literally off 6 months out off the year. My week off is like a vacation.
3) Pay varies wildly depending on company and location. Average pay is in the 70s. You can approach 6 figures if you volunteer for overtime and live in an area that has an extra stipend for location. Overtime is abundant because we're always short pilots. I never volunteer because I like my week off.
4) You won't take a flight that takes you more than 14 hrs of shift. It'll screw up your 10 hr rest period if you do. We take flights over 12 hrs duty on occasion. Just did one last night. I worked 7pm to 730am. Flew back to base to a rising sun. Yes, you get time & half overtime pay. Double time for holiday pay.
Three primary reasons why I chose RW air ambulance. First, location, location, location. Plenty of RW jobs around the country. Pick an area you want to live and go there. My company alone offered me 7 different locations around the country. I picked an area where family was. Second, single pilot demanding modes of flight. You're not sitting in a dual pilot FW typing on an FMS and going from A to B. You're landing to some road intersection in the middle of the night. There's no weather reporting for a road intersection. It's not TERPd out for obstructions. You're scanning left and right looking through a green funnel (NVGs). You don't have someone sitting next to you backing you up on call outs. It's a completely different kind of flying compared to most FW jobs. Very hands on rapid decision making. Finally, the schedule is awesome. Home every night with no lay overs and 7 days / nights on is pretty easy. I could be watching TV all night or on the Internet (I'm at work now). Very little management interaction and very little paper work. I get paid to transport the patient. That's it. It's a job where I really don't mind going into work at the beginning of the week and I'm not praying for "Friday" to come around either. Not too many jobs you can say that about.
I'm not going to sit here and tell it's the best job in the world either. It's not for everyone. We have at least one pilot that washes out during 135 training. Usually have a few that quit early on once they get to their base. I know of pilots that are anti social and can't get along with their crew. I know of pilots who were fired within 2 weeks because they scared the crap out of their crew. Your crew will get you fired in a heart beat if they don't trust you. With an historically, somewhat high accident rate, can't say I blame them.
You'll also see things, at least on the SE helicopters that aren't pleasant. You have a patient's legs sitting 2 ft to your left. Vehicular injuries can do some devastating things to the human body. Be a professional. Realize these patients are in a condition they'd never thought they'd be in. They're going through the worst thing in their lives and you need to make the flight as smooth and expeditious as possible so they can recieve life saving treatment. Mortality is in your face on a daily basis and you will have those that pass while on board your aircraft. It happens. For those that can't handle the above emotionally, well they seek employment elsewhere.
Oh yeah, the people (nurse / paramedic) in the back of my aircraft are some of the best trained most talented people I've ever worked with.
Edit: I see you did say you were considering the FW route. Disregard.