Rules say that a docked ship, upon emergency deploying, suffers a crit damage. But if that ship has shields, like nashtah pup, the crit would just knock out a shield right?

Yes.

suffer is just like getting hit during an attack... shields first then hull

now if it said "dealt a crit" or "dealt a face up card," that's different

It’s one of the reasons it so cheap , plus correct me if I’m wrong but if the nashtah pup cant deploy due to say an asteroid or ship it is destroyed.

Incorrect. An asteroid would not block deployment. A ship would only if the chosen deployment manoeuvre was blocked and there was no space to place the pup in between.