The goal is to "half" the point. You want to find the point Q where 2Q = P, your original point.

So you compute 2^-1 (mod n) where n is the order of the group (see the secp256k1 parameters: https://en.bitcoin.it/wiki/Secp256k1)

2^1 is the multiplicative inverse of 2 (mod n). 2 x 2^1 = 1 (mod n). When you do the scalar multiplication it cancels out a factor of 2.

2Q = P

(2^-1)2Q = (2^-1)P

Q = (2^-1)P

Hope that makes sense.

Sure, just multiply the point by 2^-1 (mod n).