Even if they could stop people from aging, I don't think it would effect longevity past a certain point. The body will still wear out. The heart, kidneys other fairly important organs all have a finite lifespan. What this would do is make living to be 108 a whole lot more enjoyable.
But the body wearing out is aging, not just the appearance on the outside. The kidneys and other organs aging will be able to be reversed. The general rules of aging apply to everything in the body. If you can stop one thing from aging, you can in theory stop the aging of anything else. (I think)
In some cases, yes. However, the kidneys, for example, take damage from the very act that they perform. In some of these organs, it's not a matter of wearing out, it's a function of being used up. You might be able to stop decay, but depletion is a different story.
The aging process on a cellular level has a huge number of effects, many of which are poorly understood, if at all. But if senescence were stopped, most diploid cell types (including specialized cells that make up specific tissues and organs) would continue to undergo mitosis and proliferate indefinitely, and thus not "deplete", etc.
Research regarding stem cell use could be used in tandem to address other problems, as they can be differentiated in practically any way as necessary.
Disease, particularly cancer, would persist, and probably increase (in the case of cancer). At this point, the longer you're around, the more likely you are to experience one or more of the many mutations/exposures that lead to cancer. Cellular aging is one of the body's ways of protecting against cancer.
-J