Translation:Please do not look at magazines at school.
With the word 'the,' you are referring to a delimited set of magazines, presumed by the speaker to be understood by the listener, whereas Duo's statement is general. Because Japanese lacks articles, as well as generally lacking specificity with regard to singular / plural, we might think what's the difference for Japanese speakers. The set might be indicated by a determiner or something a little more spelled out, if not clear from context: その雑誌、こういう雑誌、あそこの雑誌、つくえにある雑誌 ....
It's て directly after the stem of a vowel stem (=ichidan) verb, but after adding -ない- to any verb it's always で. There is another negative て form, -なくて, but you can't use in a command. That one takes て instead of で because the -k- in the syllable before it is an unvoiced consonant. There are a couple of tables in the Wikipedia article on Japanese verb conjugation that may be helpful, one of which is a PDF review sheet that you could download for quick reference: https://en.m.wikipedia.org/wiki/Japanese_verb_conjugation
Depending on the context, 見る can be translated not only as 'see,' but also as 'look at' or 'watch.' It's important when learning another language to realize that words in any language may have multiple meanings or uses and that you should not always expect a simple one to one correspondence of one word in a language to just one in another.