Can I legally run utility's "Water" on a granted right of ingres and egress?

Answer 1

No, probably not. That would require a different easement. The right of ingress and egress is the right of access to your property.

Say, you property was land-locked and you did not border a street. Ingress and egress gives you the right to cross a neighbor's property to get you yours. The easement prohibits them from blocking you or placing obstacles to your access.

However, if you have the easement documents available, you can scrutinize them to find if such an easement has been granted. In some cases, the easement may be unusually broad and grant you an easement for utilities.

Now, everything said, you may be able to get an easement for utilities for little of nothing. It could simply cost you the price of reseeding the ground. Some of the new diggers actually cut a slit in the ground and insert the pipe without digging a trench, but if you live in a freeze zone, that type of installation would not work.

Good Luck