Sometimes there is no difference, but other times there is. For example, "a small cat" = "a little cat." Here, they function as synonyms and can be used interchangeably.
But little can also be used somewhat differently when referring to amounts: "We only have a little bread left," meaning "not much" or "a small amount"; or "There is little reason to worry, because you have prepared well for your exam." In the examples in this second paragraph, small cannot be substituted for little.
Kuzu - lamb/the lamb/a lamb
Bir kuzu - a lamb/one lamb
Kuzuyu - the lamb (only when it is recieving the action)
Köpek - dog/the dog/a dog
Bir köpek - a dog/one dog
Köpeği - the dog (only when it is recieving the action)
Hope that helped!
Sources: Duolingo and my Turkish friend :D
You need some article per se (unless "küçük kuzu" is used as a name, for example, a character "Little Lamb" in a play). As far as I understand from other discussions, the indefinite article is mandatory whenever the noun is accompanied by an adjective (and then preceeds the noun - küçük bir kuzu). When there is no indefinite article, the definite article is implied, which makes it "THE little lamb" and "THE big dog". Was that your question?
Both are considered "round" (according to the shape of our lips when we pronounce them). But u is considered a "back vowel," while ü is "front." The difference is in the shape of our mouths when we speak them. (You can read all about vowel phonetics here: https://en.wikipedia.org/wiki/Back_vowel.)
Not to confuse things, but in French, the letter u is normally pronounced more or less like the Turkish ü. In learning French, students are often taught to form an "ee" sound with their mouths, but then round their lips; this approach might help you with the Turkish ü. By contrast, English group (Turkish grup) have about the same vowel sound, formed at the back of the mouth, with no "ee" formation.