does birthing pod have summoning sickness?

[Levi]

does a birthing pod have summoning sickness first turn?

[Arix]

Technically, yes. However, since it isn't a creature, it isn't affected by it.

[Levi]

so it can put creature out first turn?

[Arix]

Yes.

[Levi]

ok also just to be sure:
can the birthing pod sacrifice a creature with summoning sickness?
does the creature put into battlefield with birthing pod has summoning sickness himself?

[Kenji]

The rule informally known as "summoning sickness" does not affect a creature's ability to be sacrificed:

Summoning Sickness Rule
Informal term for a player’s inability to attack with a creature or to activate its abilities that include the tap
symbol or the untap symbol unless the creature has been under that player’s control since the beginning of
that player’s most recent turn. See rule 302.6. See also Haste.

The above quote should also answer your second question. Since the new creature has (obviously) not been continuously under your control since the beginning of your current turn, that new creature is indeed "summoning sick." Again, unless it has Haste, as the quote above points out.