triWox

[short birch]

does Stripe permits in-app payment
We can't say anything about in-app payment, which is a requirement from Apple and Google. If you use Stripe, integrate directly with your web, you may don't need IAP but we can't guarantee Apple/Google will or will not permit it (It's a controversial topic and largely depends on which service you provide)

an Stripe work as conductor for the different element of the project to manage the memberships and centralize the logic
No, you should own and control your membership logic on your database, and only rely on Stripe about Payment information