At least the reduction of "du" to "-te", and "Sie" to "-se" is so widespread in spoken German that every student of the German language likely will hear them as soon as she/he speaks to a native German, or travels to Germany.
They even found their way into the dictionaries (Duden: haste) or became part of a proverb:
"Haste was dann biste was"
Other such reductions may be harder to hear (and thus to learn) as they are heavily influenced by regional dialects. To illustrate this further here is the Swabian variants of "haste" (hast du) and "hamse" (haben Sie):
hasch / hosch / häsch - habetse / hendse / hender (yes this is regionally different even within Swabia)
Such reductions within a dialect will probably be understood by a student of German no less than by a native German who grew up with another dialect. Even Germans will not understand the dialect of another region without practice.
This also is why Germans usually do not actively use reductions from another dialect in speech (e.g. "hammer" will be "ham wa" in Berlin). Therefore I believe it is perfectly fine for a student of the German language (and will mostly go unnoticed) if you did not learn how to use them. It definitely is better to speak accurately.
The same holds true for native Germans talking to learners. You should avoid contractions if you want to be understood but a more advanced learner will likely know about common contractions. After listening to conversations, or when learning by watching movies they will have heard them.