I do not know exactly what the code says, but I do know what makes sense
from a safety perspective. The neutrals of all circuits should be
connected to ground at ONLY one place - in your main service panel. There
must be no grounding of neutrals in sub panels. Ranges etc. connected to
sub panel circuts should use a 4 pin connector (hot, hot, neutral, ground).

The ground wire from your main panel may be connected to multiple grounds
and it's best if these are close together. Two grounding rods are
frequently used for a lower resistance ground path and better reliability.

Do not ever use a pipe as a ground. The water supply line may be PVC or
may be changed to PVC at some time in the future and you would have no
ground.

Since a good ground is so important, use the gauge wire required by code or
larger, protect it where required and never allow a splice in it. Use only
the best quality U/L approved grounding clamps and be sure all contacting
surfaces are clean and tight.

All of this applies to your generator too. For best safety, if your
generator is outside, it should be physically close to your system ground.

If the code requires anything less, it should be changed.