Selfsame Simulacrum becomes an aura (not a minion), since that's the actual text on the animated aura. As soon as Selfsame Simulacrum is an aura, it expands to its proper size based on card text (and default aura rules), and must continue to occupy the location that was specified during casting.

Can it enter the realm Submerged if it copies a Submerged minion (or Voidwalk, or Burrowing)?

No. When you cast a minion spell, you specify where the minion will enter the realm at time of casting. When the minion actually enters the realm (i.e. it's summoned), that's when Selfsame Simulacrum's copy ability applies. Without Submerge / Burrowing / when it's cast, Selfsame Simulacrum can't use those abilities to change where it's summoned.

Does it copy Genesis abilities?

Yes.

What if it loses its abilities (e.g. Silence aura)?

Selfsame Simulacrum remains a copy, but any abilities that were printed on the original copy are now ignored.

Voidwalk