is there a reason to establish all 3 entities (LP GP and ManCo) at once and at the first close or I can register a DE LLC for ManCo now and start marketing the brand and the mission without talking about the fund?
Do not register any entities until you’re ready to start closing. This is a major mistake. MAJOR.
All 3 entities will need very specific operating agreements and they need to have relationships. It will be so hard for you to fix this mistake that you will likely need to throw it way and start from scratch.