Is 1000 thread count really better than 400?

Not necessarily. Above roughly 400, counts are often boosted by counting each ply of a multi-ply yarn, so a 1000 count can be a 250-count yarn woven four-ply. Judge by feel and weight, not the number alone.

Will the fitted sheet fit a thick mattress?

It is sold as a deep pocket fitted sheet, so it is cut for mattresses deeper than standard. Check the pocket depth against your mattress plus any topper before buying.

Does it include pillowcases?

The set is listed as a flat sheet and a fitted sheet. Confirm with the seller whether pillowcases are included, since many sheet sets add them and this listing does not show them.

Is it hot to sleep on?

Dense cotton at this thread count traps more warmth than a light percale. Hot sleepers usually do better with a lower-count, breathable weave.

How should I wash white cotton sheets?

Machine wash warm with like colors and tumble dry low. Avoid high heat, which shrinks cotton and sets wrinkles, and skip chlorine bleach on a regular basis.