Does the copy obtained using the spell simulacrum also copy all proficiencies and class features (such as the ones obtained through one's school of magic) of the original humanoid/beast?
Yes - class features and proficiencies are included in a creature's statistics
...it has half the creature's hit point maximum and is formed without any equipment. Otherwise, the illusion uses all the statistics of the creature it duplicates.
A creature's statistics includes all of its abilities, features, and proficiencies according to the extensive list in the monster manual. In that list, proficiencies are under "Skills" (p. 8) and features are under "Special Traits" (p. 10).
Jeremy Crawford also confirms that class features and abilities are considered "statistics" for a PC here:
Q: Does a wizard retains all his casting abilities, class features, feats; after casting True Polymorph (Planetar) on himself?
A: True polymorph replaces the game statistics of the target with those of the new creature. The target's features don't carry over.
Additionally, if a simulacrum did not inherit a creature's features, there would be no way for it to gain the ability to cast spells, for example. But we know it can since the spell says:
nor can it regain expended spell slots
So, yes the simulacrum you created will have class features and proficiencies of the creature it duplicated.