"I do not want to run in the race."
Translation:Nie chcę biec w wyścigu.
Biec refers to a single, completed action of running, whereas biegać refers to a repetitive action
so 'biec' is perfective, and 'biegać' & 'biegnąć' are imperfective?
If so, what's the diffence between them?
Not exactly. All of them are imperfective (they don't mention anything about reaching any destination, they're just about the process of running). "biegnąć" and "biec" are, I believe, perfect synonyms with identical forms (that's a strange thing to have two infinitive variants) and refer to running right now: "to be running". "biegać" is habitual, so it's "to run".