Some basic questions related to electricity Note These questions may be incorrect.
1) Why do positive charges flow from high potential to lower, but the electrons do not? Am I wrong?
2) Does battery supply charge to a conductor? I read it from a Youtube video.
3) If I increase the potential or charge of a conductor, will the capacitance of the conductor change?
 A: 
1) Why do positive charges flow from high potential to lower, but the electrons do not? Am I wrong?

Imagine potential as a topographical map, positive charge flow from high to low potential for the a similar reason that a river flows from high mountain to a low valley. Electrons do not since they have negative charge so they are like helium balloons and see the potential the other way around, they want to flow from low potential to high potential so flow in the opposite direction.
2) Does battery supply charge to a conductor? I read it from a Youtube video.
A battery sets up a high potential at one end and a low potential at the other end. It releases negativity charged electrons in the low potential end. They will flow through the wire and back in the high end. So a battery does not loose or gain net charge in operation. (Electrons usually don't make the full round trip back to the positive end but that doesn't matter since electrons are indistinguishable)
3) If I increase the potential or charge of a conductor, will the capacitance of the conductor change?
First: potential and charge are different. Charge is the amount of charged particles and potential is how much energy that charge has and can be used to describe how a charge will move.

will the capacitance of the conductor change?

No
A conductor on its own does not have any capacitance. Capacitance of a parallel plate capacitor is given by:
$$
C=\frac{\epsilon A}{d}
$$
Where:
$C$ is the capacitance
$\epsilon$ is a constant that depends on the material between the plates
$A$ is the surface area of the plates
$d$ is the distance between the plates
So if you have one conductor you do not have a capacitance. However it will have an extremely small capacitance with everything else in the universe, but only things very close are relevant since it diminishes with distance.
