Does it turn into a Monster minion?
Yes. It becomes a minion with the Monster type, and no longer a site.
If the flooded Rubble gets replaced with a site, is the new site also flooded?
No.
When it awakens, is it summoning sick?
Assuming it was in the realm prior to the turn it awakened, it is not summoning sick (since it was already under your control prior to this turn).
Is the ability optional?
Yes. It is an activated ability with no cost and a threshold requirement. Like all activated abilities, you can only activate it during your Main Phase when nothing else is happening, but you are not required to activate it.
Does it continue to provide water affinity after it transforms into a Monster?
What happens if you copy this after it has transformed?
Since transform effects permanently change the characteristics of the card, as opposed to temporary modifications of characteristics (i.e. Overpower), the copy effect will take on those new characteristics. For instance, a Selfsame Simulacrum copying an Island Leviathan that has been transformed will enter play as an 8-power Monster minion that provides one water affinity.
Market
$0.63
Low
$0.20
Median
$0.65