QI bloomed a Debut holomem [Houshou Marine] on my stage to hBP02-032[Houshou Marine]. At this point, I did not use the bloom effect "Houshou's Pirate Crew". After that, I used hBP06-090[Bloom Stage] during the same turn, and bloomed my hBP02-032[Houshou Marine] to another hBP02-032[Houshou Marine]. During this second bloom, can I use the bloom effect "Houshou's Pirate Crew"?

ANo, you cannot.
A bloom effect's activation is mandatory, so it was regarded that you have already used the bloom effect [Houshou's Pirate Crew] during the first bloom.
As such, "you may only use bloom effect "Houshou's Pirate Crew" once per turn" will take effect, and bloom effect [Houshou's Pirate Crew] cannot be used in the same turn.

QI bloomed a Debut holomem on my stage to 1st holomem. After that, I used hBP06-090[Bloom Stage] and bloomed that 1st holomem to another 1st holomem.
In the case that I have used hBP06-008[Natsuiro Matsuri]'s SP Oshi skill "I Absolutely Want to Win!!!!!!!" this turn, can I use hBP06-090[Bloom Stage] and bloom that 1st holomem one more time?

ANo, you cannot.
hBP06-090[Bloom Stage] can only bloom a 1st holomem again with a Debut holomem stacked directly under it.