If I refer to the cup of the coffee, can I say "Jag vill har svartt kaffe." ?
I don't know exactly what you mean, but "vill har" never works. It's "jag har" or "jag vill ha". Note also that "svart" doesn't change, I mean that you don't add a "t" with the t-nouns.
So you can say "Jag vill ha svart kaffe" (kaffe generally is a t-word) or "Jag vill ha en svart kaffe" (if you refer to a cup of black coffee).
Jag vill ha starkt kaffe.
Jag vill ha en stark kaffe.
"Vita" is still used for plural nouns, but the singular also distinguishes between common and neuter nouns - common nouns use "vit" and neuter nouns use "vitt".