Is there any positive or negative connotation in Polish for the word "few"?
In English, A FEW typically has a neutral/positive connotation: "John likes going to school. He has a few friends there." But FEW (without "a") has a negative connotation: "John hates going to school. He has few friends there."
I personally feel like "mało" is mostly negative, like there should be more. There is also "niewielu"/niewiele that literally means "not many" and it is sometimes more positive,
kilku/kilka/kilkoro - means "more than 2 less than 11", only for countable nouns and is most used for "a few" in the first meaning. There is also trochę =some that is mostly for uncountable nouns.
Does 'friends' have the genitive case here because the sentence "Mam mało przyjaciół" literally mean : ' I have a few (of) friends' ??
and if it's true, does this happen with all adverbs or just some? ."
Edit: after looking at other exercises i have noticed that anything referring to quantity is followed by the genitive case. this is also true with numbers right?
example:when saying 'two bottles, or five cars' , should bottles and cars be in the genitive form?
It's not an adverb, but a quantifier(„liczebnik nieokreślony”) and as for why:
'Quantifiers that always take the genitive of nouns include dużo ("much, many"), mało ("few, little"), więcej ("more"), mniej ("less") (also najwięcej/najmniej "most/least"), trochę ("a bit"), pełno ("plenty, a lot").'
 And as for your edit, it's not that simple:
When a numeral modifies a noun, the numeral takes the expected case, but the noun may not; also the gender and number of the resulting noun phrase may not correspond to that of the noun. The following rules apply:
The numeral jeden (1) behaves as an ordinary adjective, and no special rules apply. It can even be used in the plural, for example to mean "some" (and not others), or to mean "one" with pluralia tantum, e.g. jedne drzwi "one door" (drzwi has no singular).
After the numerals dwa (dwie), trzy, cztery (2, 3, 4), and compound numbers ending with them (22, 23, 24, etc. but not ending in 11, 12, 13, 14 in any hundred), the noun is plural and takes the same case as the numeral, and the resulting noun phrase is plural (e.g. 104 koty stały, "104 cats stood").
With other numbers (5, 6, etc., 20, 21, 25, etc.), if the numeral is nominative or accusative, the noun takes the genitive plural form, and the resulting noun phrase is neuter singular (e.g. 5 kotów stało, "5 cats stood").
With the masculine personal plural forms of numbers (as given in the morphology article section), the rule given above – that if the numeral is nominative or accusative the noun is genitive plural, and the resulting phrase is neuter singular – applies to all numbers other than 1 (as in trzech mężczyzn przyszło, "three men came"), unless the alternative nominative forms dwaj, trzej, czterej (for 2, 3, 4) are used (these take nominative nouns and form a masculine plural phrase).
If the numeral is in the genitive, dative, instrumental or locative, the noun takes the same case as the numeral (except sometimes in the case of numbers that end with the nouns for 1000 and higher quantities, which often take a genitive noun regardless).