I had the service tire monitor problem back in the spring. It happened before I had my winter tires (I live in southwestern Ontario in Canada) taken off. The SVC Monitor signal came on, but it's because the monitors needed to be reset by a shop. They put new batteries in them and they were fine. I asked the mechanic at the time if it could've been something else and he said the sensor can also go, but normally it's just the batteries that need to be reset. If there's a specific mechanic you trust, I'd go and see them.
I haven't had an issue with the service air bag, but it sounds like a sensor might not be working. Have you had a code reader on the car to pull up a possible code? A lot of parts stores offer that for free, they won't clear the codes but they'll scan it. It gives you a more specific idea of what's wrong. I wouldn't say an airbag issue is a minor issue. If the sensor's not working right and you're in an accident, it might not come out. I'd definitely get that fixed.
For the noise, it sounds like it might be the wear indicator that's on most brake pads. It's a little metal strip and when it wears down, it makes a squealing sound against the rotor to let you know you should either get new brakes or at least new pads. Even if you're not braking, it'll still happen. Is it coming from one specific side of the car? When was the last time the brakes and pads were done on the car? You might get lucky and they might only need servicing, which is basically re-lube parts in the brake system and using a small hand sander to get rust off the pads. Most shops do that for between $100 to $150. I do that myself once a year in the summer. It helps your brakes last longer and only takes a few hours, or one beer per brake.
Another thing you might want to check is the belts in the engine, but only when the car's not running, obviously. If they're loose or worn, they can make noises. Do you specifically know where the noise is coming from? If it's the engine, it's likely a belt. If it's the wheels, it's likely the brakes with an outside chance of something being up with the wheel bearings.
Also, you might want to have a longer talk with the guy you bought it from. It sounds like it needed work that he neglected and is passing the buck off on you. If you're having possible tire monitor, airbag and brakes issues, he might've been trying to dump the car while he still could. I'd hate to see you buy the used car then have to put a few hundred dollars of repairs into it less than a month after buying it.
Let us know and we can narrow down the options!