Can you please tell me why "The hotel lies at a short distance from the beach" is wrong?

Here are some more words I'd like you to check with reference to fashion.

1) wedge-heeled shoes, ParĂ -rubber shoes, trousers with patches on both sides, jeans with orange seams.
2) Can a long-sleeved shirt have a crew-neck? How do you call a long-sleeved T-shirt with a round-neck women usually wear under the jacket? (This is a real question).
3) Does "tuxedo" mean a black man's suit or just a black jacket?
Whad do you call a woman's suit (jacket+ trousers or skirt?).
4) Does a "plain jacket" mean "a one-color jacket?
What do you call a pair of torn-off (with holes) jeans?

"The hotel lies a short distance from the beach" -- you don't need "at."

1) wedge-heeled shoes, rubber-soled shoes, trousers with patches on both sides, jeans with orange seams.

2) Can a long-sleeved shirt have a crew-neck? How do you call a long-sleeved T-shirt with a round-neck women usually wear under the jacket? Yes, long-sleeved shirts with crew or round necks can be called sweatshirts (if they're made of fleece). The ones worn under jackets can be called long-sleeved tops or long-sleeved T-shirts.

3) Does "tuxedo" mean a man's black suit? Yes
Whad do you call a woman's suit (jacket+ trousers or skirt?). These are commonly referred to as business suits or women's business suits.

4) Does a "plain jacket" mean "a one-color jacket? Yes
What do you call a pair of torn-off (with holes) jeans? Ripped jeans; if they've been cut off around the knees, they're called cut-offs.