Is the use of ось similar to French voilà or voici?
voici - ось, voilà - он
How does ось differ from тут?
You use ось when you can point to the object with your hand, it's right here. It's usually translated as "here it is", "here you are" or maybe "over here"
I suspected that was the case when I checked the dictionary and it said that it can mean also "there" (like "over there"). Is that correct?
Technically, there's another word for this: он.
That's more like the french voila as opposed to voici
Does ключ always mean [one] key? or is it like rice and картопля?
Good question. Unlike рис, картопля, and other non-count nouns (often substances), ключ is a count noun, just like in English. The plural is ключі.
In Belarusian is Вось, very similar.