Can a dentist shave down my capped tooth and put a veneer over it?

It is possible. Depending on the age & condition of the crown it may be possible to put a veneer over the old crown to match the new veneers exactly, but many times it is more prudent to put on a new crown, made by the same lab that is making the new veneers. There are some challenges to matching the color exactly when you are working with a combination of veneers and crowns.
You could, but why? While it may be possible to shave down the front of your existing crown and bond on a porcelain veneer, why would you want to do this? For about the same cost you can get a new crown, which will both look better then a crown/veneer combination and be less prone to future failure.
No. Unfortunately only a new crown and replace an old crown; a veneer could not be used to replace a crown, .
Yes he can. If the "cap" is all porcelain, it is relatively easy to bond porcelain to porcelain with significant strength. If you are going to invest in a veneer over a cap then it would be in your best interest to just replace the cap since they are usually around the same cost. To answer your question, it is definitely possible depending on the makeup of the existing crown.
Replace the cap. It is better to replace the cap instead. New ceramics that are available--especially emax--are beautiful and durable.
Yes, but... Yes that is possible, but its easier and prettier to get a brand new crown made out of all porcelain.
Sort of. Typically when you have a crown on a tooth, that requires the most shaving down of any procedures. While the crown can be removed, it would usually be replaced with another crown. If you are having an older crown removed, then there are some great new porcelains and modern materials that can make your replacement tooth look amazing! Talk with your cosmetic dentist about what you want improved.
I wouldn't. It is not easay for porcelain or composite to stick to the surface of an existing crown with out extreme heat that can not be attained in the oral cavity. Besides, the cost of the veneer is not much less than a crown so just have the crown replaced and you can have the look that you want and will last much longer.
No. If you already have a "cap" or crown (what a cap is called in the dental profession) than the tooth should already be shaved down to accommodate that crown. In that case a veneer would not be possible as a veneer is like press on nail and only covers the front of a tooth. If you are doing this because you dont like the way your crown looks, you would need a new crown.