This passage actually refers to bonding. The
reference is Article 100, which provides the definitions of
grounding and bonding. Grounding in this passage makes no sense from
a technical standpoint, so the correct word is bonding.
[250.114]. Again, we have a word misuse. The
equipment must be connected to an "equipment grounding conductor"
which is, in actuality, an equipment bonding conductor. There are a
few exceptions to this requirement, but generally it applies.
[250.118]. No. It doesn't even have to be wire.
See the 14 types of EGC in 250.118.
[250.122(A)]. Yes. It can't be smaller than shown
in Table 250.122, but doesn't need to be larger than the circuit
conductors supplying the equipment.
[250.122(F)]. Yes, if you run the ungrounded
conductors in parallel.