Do Fund Managers need to file an 83(b) for acquiring Shares in the ManCo or GP entity (via the ManCo)?

Generally speaking, no - Fund Managers do not need to file an 83(b) election with respect to acquiring Shares in the ManCo or GP entity (via the ManCo). An 83(b) election is only required when acquiring Shares that are subject to vesting over time. It is very unusual for Fund Managers to subject their Shares to vesting.