what is wrong?

I drive short distance 5 days a week, I make one trip out of town a week. Been changing the oil every 3 months since I got the car. My oil is never low, when they check it. I do not put much mileage on at all.
Where exactly is the swaybar located? Will it wreck my car if I leave it?
Also could you tell me when I can tell when I need to get my tires replaced?

So should I get the swaybar replaced before winter? How much will a job like that cost? I fill my 2 front tires at least once a month, is that a bad thing?

You probably would only need to get one or both of the swaybar mounts replaced, not replace the entire swaybar. There is one mount at each side of the subframe, and it shouldnt cost much. I would think that estimate of $90 should cover the work.
You said you added air to the front tires at least once a month? Either you are adding air more often than is needed, or the tires have a slow leak. Normally a tire that is inflated to 36 psi should not drop below 32 psi in the next 3 to 4 months. If yours drop that much in a month, thats abnormal for a tire. You can expect a drop of a few 'psi' if the weather temperature has dropped dramatically however.
It could be a minor leak at the valve stem, or at the bead of the tire (where its sits against the rim). It could also be a small nail or screw is embedded in the tread and barely sticks through to the inside. If you found a nail or screw, dont pull it out; - the tire might go flat in the next 10 minutes! If its a nail or screw stuck in it, that can be repaired. If its an old valve stem, they can be replaced. But it could also be a tire that is old and worn and just leaking out through the sidewall. In that case it will get worse. If the tires were ever driven while very low on air and got heated up to really hot - the tire can start leaking, and that isnt repairable. I would recommend you begin budgeting for a pair of new tires. Where I live the less expensive new tires would cost about $75 each, after mounting and balancing. There is a 'used tire store' near here (in Alexandria VA), where I got a decent used tire mounted and balanced on a friend's Neon for $42.
I always put my better tires on the front of the car, the older tires on the back. This is because there is less weight on the rear wheels, and having a flat or a blowout on a rear tire is not so scary or dangerous.

See rthe problem may be that the people who chose my tires put on the wrong size. They are wider than they should be too. So I think they have a harder time distributing the weight right. I get my tires rotated at the proper mileage, just mainly the drivers side that has the prob. Do you know what would be average mileage on a pair of tires? I have only had them rotated once so there is not much mileage on them at all. Maybe 5 years old? They do not look that worn either.

I dont think a tire that was bigger/wider than the regular would cause any problem, except perhaps rubbing on the inside of the splash shield when making sharp turns in parking lots; a fairly harmless event.
The tire size wouldnt affect the tire losing air or not, and the wider tire wouldnt change how the car sat, or how the weight of the car was distributed.
I dont know what typical mileage would be on your tires. Inexpensive tires should last at least 20,000 miles before being worn down to the tread-wear indicators. High quality more expensive tires might take 50,000 to get that worn.

The brand of tires I have are Warrior. I paid bout $50 for each one. They still should have put on the right size tires, I did not know they were wrong at the time. My front driver tire was at 23 psi the other day, the rest seem fine. Can I get a new tire and have it as a different size? Or will that mess up my mileage more? I really do not need all new tires.

I do not want to get new tires if I do not have to. I still need to get my swaybar job done yet. What kind of things do I need to do to make my car winter ready? Do you suggest the stuff you put in your gas line to get rid of all the moisture? To keep it from freezing.

if your tires are fairly brand new, go get the guy who you bought that tire from originally to replace it. if its still bad..it oculd be the rim.

if its fairly new also, a brand new tire shouldnt be too bad as long as its the same wear rating/temp rating etc.. or similar, anyway

but for safetys sake, get the same size tires.. you dont want one tire to be able to hold more grip when you lock your tires (braking) youre gonna go sliding sideways and stuff..

as for winter.. idk, im in hawaii :D

What does it mean if my brakes squeak from time to time? They seem to work fine. How long do brakes usually last? What parts are involved with braking?

What does it mean if my brakes squeak from time to time? They seem to work fine. How long do brakes usually last? What parts are involved with braking?
Means they are wearing down. Depends on how hard you are on them. Parts involved are the brake master cylinder, lines, caliper, rotor, brake pads and so on. All you should have to replace is the brake pads and maybe have the rotors turned.

My sister-in-law can go through a set of front brake pads in a year - which is about 15,000 miles for her. I can get about 6 to 8 years to a set of front pads, (which would be about 80,000 miles) but I drive more gently & in more rural areas, & dont have as many stoplights/stopsigns to deal with. The rear brakes, which on your car could be 'brake shoes' not 'brake pads' should last longer than the pads --- unless you forget to fully release the handbrake a couple of times. That can wear out the rear brakes real early! But if your rear brakes are the drum type, they usually dont squeal. I have had to replace broken springs in the rear of our 97 Neon. They were making an occasional grinding or clunking noise; thats how I knew to open them up to inspect.
Front brakes on your Neon are the disc brake type with brake pads. If you hear them squealing its a good idea to at least have someone look at the pads, and the rotors - to see if the pads still have some frictional material left, and that the rotors are not getting scraped. When the pads are worn out I expect to hear a soft grinding from the front when I put on the brakes. This is the metal of the rotor grinding against the metal backing of the pads. It will ruin the rotors very fast - so if you hear that noise, get new pads.

You probably noticed this right after a cold or wet time. It is usually just condensation, the oil fill cap is the highest point that opens.

I also have a small clunking sound, it sounds as it comes from the right rear side of the car. I hear it when I get in the car and also when I am going over bumpy roads and when I brake sometimes. Struts were replaced out in 02, when I got new tires. The shocks seem fine and it does not seem to bounce much either. Any ideas? I have asked other people bout it.

When you say the struts were replaced, do you mean the front struts, or the ones in back? Its fairly common to replace front struts, they get more stress on them. Rear struts is less common.
If it makes the grunt noise when you get in the car, but have not moved it - it is because the car has moved on its suspension because you got in. There would also be movement of the suspension (both front and rear) when going over bumps and when hitting the brakes. If you have a rear strut that has gotten dried out from age, it can make a low squeaking'grunting sound when the stut goes up or down. I had such a noise on a 92 Ford Escort, and after listening to it for a couple of years, I replaced that rear strut. Noise was gone. I did the work myself (it was hard on my back!), or else I would still be putting up with it.
On our familys 97 Neon there was an occasional noise from the rear when we drove it. It was also sometimes noticeable when putting on the brakes, or driving slowly with the windows down. It turned out to be some broken springs inside the brake drum in back. I got new springs and replaced them on both left and right sides of the car. The broken springs -could have- interferred with the operation of the rear brakes, but they hadnt yet done so. Luckily the front brakes have most of the stopping power.