Do teachers determine final grades manually?

It depends. Some schools provide teachers a system to calculate grades so they don't have to do it. But some have to calculate it by themselves.

Some do, some don't.

Some are required by their school to use a system - but teachers usually rebel against that by adjusting the information they enter so that it spits out the grade that they would have come up with manually anyway.

My wife has taught college English at several different schools - some have allowed her to come up with her own grading scale, while others require her to use a standardized one (there is something to be said for standardization, but like I said, teachers usually just override it anyway).

The amount of effort someone is putting out, their attitude, participation in class discussions, and the amount of improvement they show over the semester all factor into how she will grade a student.

She almost always runs across a handful every semester that try to do the bare minimum to pass (or don't even go that far) and then show up to complain when they are failing the class.

She will bend over backwards to accommodate someone who is putting forth the effort, but has extenuating circumstances (and not just lame excuses), but she will not hesitate to fail someone who is obviously trying to game the system.

The funniest is when some kid's parent shows up to complain that she's failing their kid, only to find out that their kid hasn't shown up for class, or turned in any of the assignments.