No, "olika" is the plural form of the adjective, so you can say "De talar om olika kategorier".

The form "olik" exists too, but it normally means "different from", e.g. "Den ena kategorin är olik den andra.

PS. "Olika" can also be an adverb: vi tänker olika - we think differently

The same way, so we accept both as translations. :)

Yes, but it would mean "a second category".