Child, in J.R.R. Tolkien's words

The Quenya words for child are hína and seldë (an earlier Quenya word).

The Sindarin word for child is hên (child).

Boy, in J.R.R. Tolkien's words

The Quenya words for boy or youth are seldo (boy) and nessë (youth).

The Sindarin words for youth (boy) is nîth.

Youth is a word that means a young person, but historically it seems to especially apply to a young man or boy.

Girl, in J.R.R. Tolkien's words

The Quenya words for girl are wen (girl, maid) and nettë (girl, daughter).

The Sindarin words for girl are iell (girl, daughter, maid) and sell (girl, daughter, maid).

Maiden, in J.R.R. Tolkien's words

The Quenya word for maiden is vendë (maiden, girl).

The Sindarin word for maiden is dess (young woman).

The suffix -wen also means maiden in apparently both Quenya and Sindarin. It's a frequent ending in feminine names, such as Eärwen which means "Sea-maiden".

Woman, in J.R.R. Tolkien's words

The Quenya word for woman is nís.

The Sindarin word for woman is bess (woman; wife).

Man, in J.R.R. Tolkien's words

The Quenya word for man is nér (man, adult male - elf, mortal, or of other speaking race). The Quenya word quendu means elf-man.

It seems that the Sindarin words for man is benn (man, male, husband). There's another Sindarin word, which is apparently archaic, dîr (man, adult male - elf, mortal, or of any other speaking race). The Sindarin word adan means Man as a people or a mortal man. The Sindarin word ellon means elf-man.

Person, in J.R.R. Tolkien's words

The Quenya word for person (one,(some)body, person, individual, man or woman) is quén.

There doesn't seem to be a Sindarin word for person. In Sindarin there are words for human being, as opposed to elf, which translate to follower, born later, Second People, and mortal. Not quite the same as person.