Is it breathable enough to wear while hiking on a hot sunny day for sun protection?

Yes, I believe it would be! It is light weight enough and seems to be working for what I wanted it for...I wear it into the pool, during my water aerobics class, and wanted something to feel a bit protected from the chill when the A/C comes on!

Do the sleeves inch up while swimming? Thanks

I did not notice any inching up, but when dry, the sleeves on me were a tad longer than my wrist. I found this comfortable both in & out of the water (Plus I was too busy gawking at fish to notice)!

Does this include swim bottom？

No，just the swim top，and I LOVE it!

Do you need to apply sunscreen under shirt also? And is it washable?

Yes its washable and No sunscreen underneath. love it very protection in the sun. The best investment that I bought.