1) E = (1/2)mv^{2} - ke^{2}/r (sum of kinetic(Newton's law) and potential (Coulomb's law) energy.

now, angular momentum is mvr

Bohr equates this with nh/2pi

so mvr = nh/2(pi)

third assumption: centrifugal force = centripetal force:

mv^{2}/r = e^{2}/r^{2}

by using the above two equations and substituting for r, v becomes:

v=2(pi)e^{2}/nh

where e is the charge like Z.

Square the resulting v and use it below:

kinetic energy = (1/2)mv^{2}

3) are you sure you don't mean angular momentum?

nh/2(pi)

n is the orbit , h is planck's constant.