Depends on surgery. For vision correction surgery, such as lasik, there is no restriction on lifting. Also, following modern micro-incision cataract surgery most patients can lift and bend right away. Heavy lifting - as in significant weight lifting - should probably wait a month or so until off of all eyedrops.
Yes. Heavy lifting can increase venous pressure and cause bleeding, which is potentially dangerous after eye or eyelid surgery.
Yes. Yes for at least 1-2 weeks.
Follow instructions. It is best to follow the instructions for post-operative behavior and activity given to you by your surgeon. Activity depends on the type and complexity of the surgery, so no generalizations should be made. If you are unsure, check with the surgeon!