Infinitely many.
There are many angles inside a circle. You have inscribed angles, right angles, and central angles. These angles are formed from using chords, secants, and tangents.
6
The central angle is the angle that has its vertex at the center of the circle.
To count how many different central angles a circle has, count how many different numbers there are between zero and 360. Include all of the possible fractions. You should discover that the number is very big.
Without overlapping, 4.
Yes all inscribed angles in a circle have their vertex on the circumference of the circle. Central angles have their vertex at the center of the circle.
360 degrees
Yes.
Infinite angles. If you are referring to degrees then the answer is 360, but if the question is angles I can get as many angles as I want inside a circle.
with a pencil or pen
A circle does not have any angles.