I thought that motorcycle was "motorcykl?
Either "motor" or "motocykl", no "r" in the latter.
Are there times when using either "motor" or using "motocykl" are more common or more appropriate? Such as, a style of motorcycle?
Not that I know of, but maybe someone who knows about them can say more.
Anyway, frankly, it would be better to teach "motocykl", "motor" is a bit colloquial.
I really do think it's fine to teach colloquial words here. Most of the learners just want to have conversations in Polish, not to write books ;-)
Would it be fine to say? Our bike is brown. As nickname for motorcycle
OK, it seems common enough. Added.