Would this work for school/laptop?

Yeah...but with that kind of handle you would have to hand hold it which might get old. I like being able to put mine on my shoulder....will that one fit on your shoulder?
are these bags made for laptops?

yes - you can probably put a laptop in one...but does it provide the protection (ie - cushy sides) against impact so your computer doesn't get damaged?
Which shoulder bag would you recommend to carry a laptop? Mine is 14L x 10.5W.

I have a hamptons business tote from the boutique earlier this year. I also have a messenger and large book tote from the outlets...those are both a couple years old or more...but the outlets always have some variation of both those bags.
I do okay with it on my shoulder...but do switch to the messenger if I'll be carrying it for an extended period (ie traveling through airports). But I don't put a lot of other stuff in the bag...usually my laptop, power cord, notebook, planner, pens, highlighter, lotion, some medicine bottles.