I have a manual 2001 Hyundai Elantra, and I have two problems. Help me out?

[master_prick14]

First problem:
This I've had since I got the car. I happens nearly every morning and every time I start the car from at leas four hours of being parked. I looked under the hood, and think the noise was coming from the belt. Something the belt is around is not turning (I think it is the AC, but it will make the noise even if AC is on or off). How do I fix this loud annoying squeak?

Second problem:
I was just on a drive to Target to return a CD. After I returned it, I went back to my car and started it up and went on my way to McDonald's. As I get to the stoplight, I kick it out of gear and idle behind a car, then I notice on my dash my RPM is going up high without me pressing the accelerator pedal. It idles normal, but now when I put it in neutral, I notice it go up to 2,500 and just stay there revving high. I gave it a little gas to see if it would rev up and then return to normal; no dice. It revved up to 3,500 and stayed there for a couple seconds before returning to normal. I also noticed there is a yellow light solidly lit (that wasn't lit before) on my dash that says "check" underneath a little picture of something I don't know. It looks a little like plumbing pipes with handles and valves or something? I don't know.

Anyway, I was wondering how to fix the squeak; but WAY MORE IMPORTANTLY, I'd like to find out why it revs up in neutral, what the problem is, how to fix it , and what it will cost.
Please help me.
I see the lights when the key is turned to on, and when I start, the aforementioned light stays on. I will see if the light is still on tomorrow, but I'm definitely looking to fix this asap because I don't want long-term problems. I'm not sure if the cable is sticking, because I turned it off at the drive through, and when I started it up, it revved to 2,00, and I didn't even push the throttle.

I'll check the belt, too. Squeak is annoying.
It has 144 thousand miles on it.
The red line is at 6,500.

[not 2 B fooled]

The squeak is probably a belt that is going to need replacing soon; the noise is from a condition called "glazing" where the belt surface gets shiny (look at the underside of all belts for this) The light may be a check engine light - next time you go to start it, just turn the key to the "on" setting and see the warning lights that light up; all should go out when the engine is started; any that do not indicate something that needs to be looked into further. Another possibility of the sticking throttle is the cable where it attaches to the fuel injection - it may need some lubrication at that area

[Lawn Gnome]

How many miles are on it would help. That is a itty bitty 4cyl I think the red line is at 6k or so.
PCV valve, Fuel Filter, something in the fuel system sounds off, could be an EGR or even the Fuel Pump, that is in the Fuel Cell.
My nephew had one of those, the motor had a meltdown at 280,000m, he was lucky that it was on a highway cause the car jumped off the road onto the shoulder.
2001, I would guess it has about 200k plus on it, now it is going to nickel and dime you to the poorhouse or is going to seize up and fail.
The 4d is worth or valued at $2k or so.
It may be worth doing an overhaul, or replaceing the Motor, but is going to be rough, that car is fast approaching what is known as EOL, End of Life. That is the defective by design table that many many cars have taken, they make them harder to repair and that way they sell more.