#8 copper will be fine as long as we're not talking some rediculously long run, but if the tub is outside you need a wet rated conductor like THWN. Most of the stuff you find marked THHN is also marked THWN but check to be sure before you buy.

You need to look at the installation instructions for your hot tub. You may not need the neutral wire. My spa for example doesn't require it. Just ground and two hots.

You can not just remark #8, you need to use the white (if you need the neutral) and green wires. You can't use a bare ground in this situation either.

You do know you need a GFCI as well? And a maintenance disconnect. This is usually cheaply done by getting a disconnect/GFCI breaker box called a "Spa Pack" which will run about $100 at the home centers.

The size and rating of the conduit depends on a number of factors like is it going to be exposed to sunlight, etc.... One you select an appropriate conduit type, tables in the code tell you how big it needs to be (again depending on whether you are running three or four conductors). Sizing up a little bit may make pulling a little easier.

Yes, you can go with #10 (copper) ground in this case.

It would behoove you to read ART 680 of the electrical code before wiring up a body of water you're going to put your loved ones in.

Thanks Ronnatalie! The run is between 80-100 feet. It will be exposed to the weather. It will be run under the eave of the house. Thanks for the reference to ART 680. I will start reading it tonight.