robinj is not right. The English sentence can easily refer to multiple pairs of scissors and still make sense because the subject is "we" and it is unlikely they would have all been using the same pair of scissors. We don't have to worry about this distinction in English because the singular and plural of "scissors" are the same and the ambiguity is inconsequential.
As a native english speaker I could see saying "We do not use the scissors" whether I was talking about one pair or multple pairs (say for an entire class). Whether there is one pair or multiple would depend on the context. Leaving out the "the" would sound better when not referring to a specific pair, but again it depends on context.
Technically yes, but generally I think "use" works better than "make use of". To me, "make use of" often has the implication that whatever is being used would otherwise go to waste or is a substitute for something more desirable that isn't available. It's also unnecessarily wordy in most situations.
"Schere Nicht" and "Scheren Nicht" sound almost identical because of the "n" in "nicht," and it's impossible to figure it out from the context. If a couple adjectives were added (for instance, "die grosse schwartzen Scheren" as opposed to "die grosse schwartze Schere') there would be some kind of clue.
In this sentence, including the article gives the most accurate translation, but the difference is rather subtle. With the article, we're speaking about a particular pair of scissors, but without, it would be more indicative of not using scissors at all. In that case, I would use for the German: "Wir benutzen keine Scheren."