I passed the go-live process with the help of a user of the production account who logged in to select the menctioned production account. Do I need to impersonate him from now on when sending envelopes? If he creates me a user in the production account, will I be able to send them by using my own user id, create RSA keys and so on?
No, there's no such need. If your IK (integration key) is live in production it can be now be used with any user or any account in production.
If your app already has an RSA key from production (in case you're using JWT) then you're good to go and to make API calls.
The only thing you'll need for different users is a one time initial consent. This can be provided individually - https://developers.docusign.com/platform/auth/consent/obtaining-individual-consent/, or by the organization administrator for the entire org - https://developers.docusign.com/platform/auth/consent/obtaining-admin-consent-internal/