These are all really good questions, hmmm lets see.
Sleep- Actually, we do see link sleep, in Sky Sword and Ocarina of Time 3D, the player is given the ability to sleep just by going into either your bed or another npc's bed to recover hearts, and apparently (Whilst i was researching this xD) "he technically does fall asleep during the stories Anju's Grandmother reads, and in OoT, he's put into a magical sleep within the Temple of Light for seven years".
Eat- I did not know the answer to this one, so i looked it up on Yahoo:
Link doesn't eat; he's a tree.
LOL JOKING.
Well...
Health potions ect?
Theirs Kokori salad but no proof he eats.
Their is proof in wind waker Link drinks his grandma's soup.
Fairy powder?
Bugs?
Sariah's p**sy?
Recovery hearts?
In ALttP he eats apples.
Eats Pastries in TMC
Eats soup, bees, worms and chuchu jelly in TP
Elixer soup in TWW
Zora water.
So yeah, apparent from the Sariah's thing which i don't get XD, he has eaten things before.
Bathroom- On the topic of Link going to the Bathroom, there is a theory that he does not wear underwear, and "relieves himself" whenever he goes swimming, so make sure you let him go for a dip every once in a while, otherwise you might see that his outfit does actually change colour! *wink wink*
Showering- The reason he doesn't shower is quite simple, which is due to the general time line that LoZ was set in( i think it was the middle ages), during the middle ages many men and women simply did not care about "personal hygiene" and "keeping clean" (although many historians do say that people during those times did have baths, but in a different way to many expect, apparently, i don't know that much about it XD)
Girlfriend- Considering he is always traveling, doesn't speak, doesn't "shower", goes to "relieve himself" in lakes and ponds, and is always being chased by a mob of chickens, i doubt he would be able to keep a solid relationship, especially with the first two points, as in middle ages they had no form of communication through electronic devices and such, since he travels he wouldn't be able to contact her much, and even if they were to meet up on a regular basis he wouldn't talk anyway( and having a good relationship requires good communication skills xD). The 3rd/4th reasons would put a girl off in the first place and being chased by chickens is not ideal!
I hope i could kinda give you some insights through my point of view of how Link actually functions as a human, its a bit messy but i hope you enjoyed it XD