Do side effects for venlafaxine go away quick?

Some do, some don't. Sometimes it takes a few days to get used to a new med. If side effects are mild or reasonably tolerable, your doctor may advise you to continue & see if they decrease over the first week or so. Stomach upset and a general "drugged" feeling often go away. Sexual side effects, if any, tend not to go away as often, but there are strategies to manage them if the medicine is working otherwise.
Fairly so. Generally if side effects from venlafaxine are going to go away, they'll do so within the first week or so. If nausea, it may happen each time the dose is increased -- and then dissipate.