Does installing a lift kit on a 4x4 improve the 4x4's angles of approach and departure?

What gives you more angle is getting what hinders it the most out of the way. On most vehicles the front bumper limits what angle you can take. I would say that the suspension lift is the 1st thing to do as it will lift the whole vehicle where the body lift will lift the body, but leave the bumper where is is presently. Like was stated before you will loose stability the higher you go and the driveline components you will have to watch closely as everything will be at a steeper angle i/e your driveshafts mainly.

Depends on whether you do a body or suspension lift. Suspension lift is probably what you want.

Yes, if you have a greater angle of approch then you will be able to clear larger obstacles, but raising the vehicle also raises its center of gravity making it more likely to tip over. This will also depend greatly on what vehicle you are driving.