If you have the old head off, you should not need to loosen the neck. Just put the new head on in the exact reverse method of the one you just took off.

Get the head tight BEFORE putting the bridge up. You can do any minor adjustments after that. I usually bring the head to 80% of tight before I set the strings and place my bridge.

To measure the bridge. I would look at the old head and see about how far down to place the bridge. Then, using the 12th fret, strike your harmonic. Then again at the 12th fret the note. The two notes produced should be the same pitch. If the fretted note is sharper than the harmonic, move the bridge closer to the tail piece ( making the vibrating length longer thereby flatting the sharpened note). If the fretted note is lower than the harmonic, move the bridge toward the neck ( to make the note sharper). When the two toness match in pitch, your banjo is bridge is perfectly set. At that point make any final tightening adjustments and make sure that the nuts are all tight by giving each a 1/4 turn more so that none fall off.