How many electron levels exist?
As many as the atom needs.
In reality, electron energy levels are "accessed" as soon as the electron "occupies" an orbital in a new energy level. Energy levels of empty orbitals don't really exist. We just like to say they do for simplicity, and draw, e.g.
The usual orbitals atoms have often used (grouped by angular momenta) are:
#1s, 2s, 3s, 4s, 5s, 6s, 7s#
#2p, 3p, 4p, 5p, 6p, 7p#
#3d, 4d, 5d, 6d#
No atom has so far used a