I don't know of a name for that, but you need to be more specific as the practice may entail collecting sample as a collection, for evidence, for personal use, for artificial insemination, or collecting "nasty panties" i.e. those worn home.
No one can say why for sure as with any other fetish, it's so weird it's called a fetish
Sperm
Sperm ducts
The male gamete is a sperm. The female gamete is an ova or egg.
The tail of sperm is called flagellus and it also has a centriole in the tail as well. The centriole helps and propels the sperm to swim.
A foot fetish.
An earlobe fetish.
Schediaphilia, is the word for that fetish. It is also know as toonophilia.
No one can say why for sure as with any other fetish, it's so weird it's called a fetish
Fetish for small spaces is called claustrophilia.
There isn't really a special name, probably because it is not very common. It is simply called an elbow fetish.
Remembering that fetish means replacing normal object of sexual desire with the fetish object, I suggest you are seeing the gun as a phallic symbol.
Watersports
flowers work together by collecting pollen and sperm
That is too normal to be called a fetish. Most men are intensely aroused by the female buttocks and anus.
That's so obscure I don't think there's even a name for it. I think it would just be called a report card fetish.
A coin collection is called, well, a coin collection. The hobby of collecting coins is called numismatics.