Would an electron have to absorb or release energy to jump from the second energy level to the third energy level according to Niels Bohr?
According to Bohr, the energy level nearest the nucleus, n=1, is the lowest energy shell. Successive shells are higher in energy. Your electron would have to gain energy to be promoted from n=2 to n=3 shell.
In reality, we define the energy infinitely far away from the nucleus as zero, and the actual energy of all the energy levels is negative. The n=1 (innermost) shell has the most negative energy, and the energies get larger (less negative) as we get further from the nucleus. Just the same, moving an electron from n=2 (a more negative energy level) to n=3 (a less negative energy level) requires the electron to gain energy.