If I lose weight will my breast skin tighten and will they lift back up?

Sorry no. If your breasts are sagging, further weight loss will increase this, they do not tighten up. : (.
No. Unfortunately, as you lose weight your breasts will probably shrink and if they sag now they will likely sag even more after weight loss. The only fix is a breast lift or a lift plus implants.
Not likely. One of the most common procedures after significant weight loss is breast lift, because rarely the breast tissues shrink back sufficiently.
To a limited degree. Yes but only to a limited degree which is not predictable. This is not unlike the shrinkage which occurs following cessation of lactation.
Unlikely. The supporting ligaments of the breast usually stretch and do not shrink after a period of weight gain followed by weight loss.
Ligaments loosen. The breast is partially supported by coopers ligaments. These will stretch during a weight gain or engorgement during breast feeding. Often, after prolonged stretching, the breast will lose the resilience of the ligaments. This results in breast posits, or drooping.
Maybe. What happens after you lose weight depends on the quality and elasticity of your skin. It's possible that if you lose weight, your breasts may get smaller and the skin may retract back somewhat. However, people who lose large amounts of weight often see that their breasts look deflated because the skin doesn't tighten enough when their breasts lose volume.
Yes. Shrinkage and recontouring of the breasts post-pregnancy/nursing is widely variable due to skin differences, age, elasticity, genetics, etc. It is common to lose a portion of subdermal and retroglandular fat with each pregnancy, thereby increasing the sagging of the breast tissues.