My daughter is wearing a full-body, two-piece swimsuit.
[These are usually worn as protection against the sun AKA rash guards]
full-body two-piece swimsuit or swimwear, for the little girl
In the US.
A retailer would use swimsuit for both sexes.
An older person might say swimsuit for both sexes.
An event organizer also.
Young/er people say bathing suit (for both sexes), board shorts (for men/boys, longer trunks), trunks, swim trunks.
Girls say bathing suit for what they wear (a one-piece, two-piece, tankini or bikini)/
But a young guy would not use swimsuit in speaking to another young guy.
Yesterday, after answering this question, I went to a local pizzeria (Northeast US) where I saw a group of young ladies (14 to 16). I asked them: Can you imagine one young guy saying to another: Hey, dude, did you bring your swimsuit? They all laughed and said NO very loud.
No, the word swimsuit is not used for men except generically on a website or in retailing or event organizing. Speech between men would not usually contain the word swimsuit in conversation. Swim trunks or swimming trunks or even board shorts are more accurate in every day conversation.
Swim briefs are "European look" swimwear or racing briefs.
Apparently, these briefs are making a comeback. For a number of years (in the U.S. at least), men's swim trunks became long-ish shorts.
He is wearing a speedo or swim briefs.
This answer is not a treatise on swimwear terminology. It seeks to answer the specific questions from the OP.