Learn Dutch: Het is handig als je deze kopie print. - It is handy if you print this copy.

The word als (if) is a subordinating conjunction. This means it introduces a dependent clause, which forces the conjugated verb (print) to the very end of that part of the sentence.

Could I use the phrase voor het geval dat instead of als here?

You could, and the grammar would stay exactly the same because both are subordinating conjunctions that push the verb to the end. However, the meaning changes from a direct condition (if you print this copy) to a precaution (in case you print this copy).

Since the subject is je, shouldn't the verb be printt with an extra T?

The rule for the je (you) form is usually to take the stem of the verb and add a T. But for verbs borrowed from English like printen, the stem is print. Because it already ends in a T, Dutch spelling rules say we do not add a second one. So it is just je print.

Why do we use deze instead of dit for this copy?

We use deze (this) because kopie is a de-word (de kopie). If it were a het-word, you would use dit.