How do you get a Ny'vene to be able to regenerate. I noticed that all the regen Ny'venes I saw were genetically tested, so does that make it able to regenerate?

You cannot make a ny'vene regennable- you can only buy one.
A pet that can be regenned must fall into all of the following categories:
1. it is a species that has been revamped
2. the species has had traits moved to different slots
3. it was a pet that was bred prior to the species revamp
4. the traits that the pet in question would have would, thus forth, clash with each-other or have been fundamentally altered.

In the case of Ny'venes, for instance, any ny'vene that had the M3 Essence of Fire became regennable because the trait was split into M1 Essence of Fire on the body and M2 Essence of Fire on the head.

Another example is morkkos: the ones that became regennable were the ones with Leaf Veins, as that trait was moved to a different trait slot, making any morkko that had had Leaf Veins and a G2 trait impossible.

(This guy is an example of a regenned ny'vene that hasn't been gene tested (his carried traits, despite our hand-picking them, go unseen) and this guy is still regennable but also obviously hasn't been gene tested. It just depends on if they were tested before the revamp or not- the testing carries over reguardless)