Why is 2s complement of 000 equal to 111, but 9s complement of 000 is not 888?
You are very confused due what is simply poor terminology, to be honest. Both your statements 2 and 3 are false due to the same misunderstanding.
For each base $b$ there are two mainstream variants of the 'complement', the radix complement and the diminished radix complement.
The two most common bases in computer science are base $2$ and base $10$. Confusingly, the definitions usually used are:

one's complement: the diminished radix complement of base $2$
two's complement: the radix complement of base $2$
nine's complement: the diminished radix complement of base $10$ (not $9$!)
ten's complement: the radix complement of base $10$.