Can a very wealthy person(Bill Gates,,etc.)build and use their own aircraft carrier for personal use?

no, because they are for military purpose only, and nuclear generator that powers the carrier would make for a nice bomb for terrorist if they ever seized the carrier, that is why the government would never allow it.

Yes they can. But they probably don't have enough money to do it. Generally, the cost of building an aircraft carrier is $9 billion or so (if it's fully stocked with warplanes). A civilian aircraft carrier would probably be $5 ish billion. But they'd have to have it custom built. And then they'd have to custom build jets to land on the thing (commercial jets don't have the short stopping system required to land on an aircraft carrier). And then they'd have to pay enough people to staff the thing.

The personal wealth of the richest people on earth falls short of making it a realistic project.

certainly they would not be allowed to arm it, and there would probably be various regulations they would have to deal with especially for the EPA. They couldnt build any aircraft carrier similar to what is used by the military...but some other design that fits that basic purpose might be possible with the help of a bunch of lawyers (they would cost a lot more than the engineers)

Yes. But if it or the planes were armed, they'd have to be pretty good diplomats to convince the rest of the world not to seize it. Finding a port that could and would dock it would be a pain too, not to mention that the things cost up to $9 billion, and the fuel bills would ruin them.

Yes a variety of celebrities including Bill Gates own a plane!

If the wealthy person is a Rothschild...

Why not? As long as all laws and guidelines are followed

They could try, but would probably get it bombed.

not legally in the US. there are things you can't have for security reasons.