Reading the description in context gives:
You shape an illusory duplicate of one beast or
humanoid that is within range for the entire casting
time of the spell. The duplicate is a creature, partially
real and formed from ice or snow, and it can take
actions and otherwise be affected as a normal creature. It appears to be the same as the original, but 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.
What the simulacrum is is an illusory beast or humanoid that is partially real - illusions don't heal naturally or magically.
Reading the monster manual everything is a creature - constructs, undead, beasts, huminoids etc. Being a creature does not mean it can heal naturally or magically - some creatures can and some can't.
The simulacrum has the statistics of the creature and half its hit points - it does not have any of the racial or class features except for spell slots that cannot be regained so healing surges and short rests don't come into it.
If the simulacrum is damaged, you can repair it ...
You can repair it - you can't heal it.
No.
Trivially, the spell text does not say that a simulacrum knows what its "original" knows. Spells only do what they say they do, so the simulacrum doesn't know what the original knows.
For instance, the Clone spell explicitly states that the soul-infused clone keeps its memories (emphasis added):
The clone is physically identical to the original and has the same personality, memories, and abilities, but none of the original’s equipment.
Simulacrum does not have this language, so it doesn't retain its memories. It's also worth noting that this text delineates between three key aspects of a character: personality, memories, and abilities. While a simulacrum might know just enough to use its abilities, as detailed by its game statistics, it would not have memories like the location of the cult's secret HQ.
Other support:
It's not specifically stated in the spell, but the wording of the spell suggests that the simulacrum is a different creature that has the same game statistics and appearance as the original.
Below, I've bolded the places in the spell that show how the duplicate is different from the original:
You shape an illusory duplicate of one beast or humanoid that is within range for the entire Casting Time of the spell. The duplicate is a creature, partially real and formed from ice or snow, and it can take actions and otherwise be affected as a normal creature. It appears to be the same as the original, but it has half the creature's hit point maximum and is formed without any Equipment.
Thus, the simulacrum has the appearance of the original creature, but nothing else.
Moreover, just because two creatures have the same game statistics doesn't mean they have the same knowledge--you can have two wizards that have the same stats but different knowledge, for example.
As for spells, as you point out, the text refers to expended spell slots, which seems to assume that the simulacrum does keep the spellcasting class feature of its original.
Best Answer
Yes, because the simulacrum is a creature.
The points you present are plausible reasons for why a DM might disallow cloning a simulacrum in their own campaign setting, but a strict reading of the rules shows that you can clone a simulacrum.
Specifically, the simulacrum spell states:
And the clone spell acts on creatures:
Because the simulacrum is specifically a living creature, it is a valid target for the clone spell.