"No woman likes him."
Translation:Keine Frau mag ihn.
ihn is Akkusativ (direct object) and ihm is Dativ (indirect object)
A few verbs take Dativ, for instance helfen:
Keine Frau hilft ihm
gern gives the meaning you do the verb with pleasure. gern doesn't mean to like.
Anyone can tell me if it would be okay to say "Keine Frauen mögen ihn"? Is there any difference in the meaning besides the singular form change into plural?
"Ihn" is accusative case while "ihm" is dative case. If you don't know what accusative and dative mean, I'm pretty sure you can easily find a good explation for it with a google search.