So, since Killmonger always seems to be able to defeat the Black Panther...could he defeat the Batman as well? (especially since Batman is less powerful than the Black Panther?)

Sure. Actually, T'challa beat Killmonger during Ironman Annual 5.
Batman has better feats...because he has hundreds more showings....but Killmonger *IS* superhuman and he is also a genius.

He would give Bruce a hard time...and during Jungle Action, T'challa fought a entire army before he even got to Erik...

I really think KM would give Bruce a serious run for his money. The only thing people might use against him is his lack of feats compared to Bruce.