I agree that tear is just the dust cover and will not cause a leak. Do you have a MityVac or other vacuum pump and gauge you can connect to the booster vacuum port? I would test the booster by itself first. May take quite a few pumps with a MityVac but the booster should build vacuum and hold it for a while. This would definitely tell you if it is the booster.

When you tested the vacuum pump, did you put a tee in the line to the booster or disconnect the booster and put the gauge directly into the line going to the pump? If you check it without the tee first to verify the pump is working, then put the tee in and you don't have enough vacuum, that would also tell you the booster or seal between the booster and master cylinder is leaking.