The actual situation that Jake ends up in after Roland left him behind is...a little odd, primarily because of other events later in book 2, The Drawing of the Three. It's not exactly like "nothing happened to him". But without spoiling too much, rest assured that Jake will make a comeback to the Dark Tower series, specifically in book 3 The Waste Lands, and from then on stays a major character throughout the whole story.
The events of The Gunslinger, specifically Roland leaving him behind, will however still remain to stand between Jake and Roland for quite some time, though, even if more on a deeper emotional level and less as a direct conflict. It's not like he just forgives him right away. But you will notice that Roland doesn't always show himself from his best side in his quest for the Tower, yet his companions largely manage to deal with it and stay with him nevertheless. He is to a large degree a bit of an anti-hero.
However, Roland's actions don't go without effect on him either and he does feel guilty about what he did to Jake. But remorse on the other hand is a different question, since Roland is also a very stubborn character and he is convinced that the things he does to reach the Tower, how bad they might be, are necessary, since the quest for the Tower is everything for him.
With regards to Roland's redemption, that's...a bit of an overarching theme throughout the entire series, so I'd hesitate to delve too much into details. But Roland will to some degree make a development in his character and realize the errors in some of his ways, specifically also in his relationship to Jake. The two will also ultimately make peace about what Roland did.
This is all a little vague, but if you keep reading, all your concerns will be adressed significantly.