1) "Sail on a boat" is natural. 2) "Sail on a sailboat" is more natural. 3) "Enjoy a good time there" is natural. 4) "I offered it to you" is correct and natural. "I offered it for you" is incorrect. "I can make you an offer" is another way to say it. I'm a U.S. native speaker. I'm not 100% sure of British usage on these next three. These are U.S. answers. 5) "Have a swim on the beach" is wrong; "Have a swim at the beach" is correct. These sentences all make sense: "We had a nice time at the beach yesterday. We played volleyball, at the beach. We swam at the beach. We built sand castles at the beach. We play volleyball on the beach. We swam in the ocean. We built sand castles on the beach. We dug in the sand and made sand castles." The phrases with "at" refer to the beach as a place, rather than as a piece of sandy land. "We were at the beach the other day." "Oh, which one?" "We were at Dennis. We were at our folks' place on Cape Cod." 6) "I went into a ride at the funfair." No, at least not U.S. usage, we would always say "I went on a ride..." 7) "I went for some rides at the funfair." OK, but "I went on some rides" is more natural.