Student or Learner
P1: Hey do you want some icecream
P2: Nah, i'm fine
P1: C'mon just take a taste from me
Come on, just have a little taste!
Go on, have a taste.
Have a taste of mine.
I think "Have a taste from me" sounds (a little) like you're suggesting that the other person actually shares the ice cream that is already in your mouth!!!
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
When we use "have a" ...?
(Speaking of tasting and sharing food, my own Mother used to let Sparky the cat lick her ice cream cone, but she wouldn't eat off of the same fork as me if I offered her a taste of my food. Me, her own first-born child. )