Non-academic is a simple neutral statement of allegiance. Non-academic experience is one you gain outside of school. Non-academic license for software is different than "software for educational use only".
Unacademic is inappropriate for academic standards. A paper that calls upon results of Tarot readings as source of prediction of construction durability is unacademic. The theory of Intelligent Design is unacademic.
"Mandatory" means that the thing must be done due to some reason or rule.
These courses are mandatory.
That is, you must take the courses or else you fail.
Wearing helmets was made mandatory a few years ago.
It is a rule that you must wear helmets.
"Indispensable" is that the thing is so critical, useful, or important that you cannot conceivably throw the thing away.
The volunteers' help was indispensible.
The mission would have failed if the volunteers didn't help.
He made himself indispensible to the parish priest.
He was deemed a must-have person because of some good quality.
These great tools are so versatile that they are indispensable.
The tools are so good that you shouldn't be without them.
To sum up, these two words are not interchangeable - they have their own distinct meanings.
Best Answer
When I looked up supple in NOAD, it said, "See note at flexible." Here is that note:
There may be some exceptions, but, as a general rule, supple applies more to skin, fabrics, and materials.
In other words, a flexible hose would be easy to bend or coil, while a supple hose would be easy to pinch or crimp.