Why で instead of て?
It looks like で is used for negative verbs when in ない form
ないで下さい is a phrase that means 'please do not'.
It gave me 「行かないで」and then 「行か」「ない」and「で」separately... Why?? XD
Confusion purposes.. Perhaps?
Yes, either one is accepted. Clicking on them separately or clicking on the pre-populated one. It's there so you know what you translating.
Why might it prefer がっこう に行く instead of がっこう へ 行く?
I don't think duo acknowledges へ existing as a particular outside one lesson.
What is the difference between まだ学校に行かないでください and 学校へまで行かないでください?
(The latter was accepted for me, but I don't understand what the difference is.)
I think, ne highlights the school and the he highlights the WAY to school. Or something like that!