Paper airplanes are like real airplanes in their basic physics. Some points:
They should be mildly nose-heavy. (The tail actually presses downward, to counteract the nose-heaviness.) If they are too nose-heavy, they will just arrow into the ground.
If they are tail heavy, they will go up, and then slide backward.
If they are neutral-balanced, they will go up and down with a scalloped motion.
If they are mildly nose-heavy, they will be stable, because if they slow down, the nose will drop, which makes them go faster, thus more lift, which brings the nose back up.
The speed is determined by how much up-elevator you put on the back.
If you put a lot of up-elevator, they will tend to turn up, which slows them down, so they will be stable at a slower speed.
If you put neutral elevator, they will have to be going much faster to bring the nose up, so they will tend to fly faster.
A paper airplane, like any airplane, will always descend unless something is pushing it.
That's because by descending it is using gravity to overcome its drag and keep its speed up.
If you want it to stay up longer, trim the elevator up so that it travels more slowly.
Also, anything you can do to reduce drag will help it stay up.
If you want it to go in a straight line, rather than turn, all you can do is try to balance it left-to-right.
That's a problem with airplanes in general.
There's very little you can do to make them stable in the roll axis.
That's why when pilots wander into clouds, where they can't see a horizon, they can easily get into a spiral, unless they can keep the wings level by trusting their instruments.