I've never heard of such a thing. For me, it's always been a choice of funds (and maybe company stock) held at a brokerage that allows me to reallocate investments as I wish.
I have to believe that if a company is "managing" 401k investments, it's just an abstraction on top of some agreed-to investment strategy at the brokerage.
Depends on what you mean by "manage". The money is explicitly yours, the company can never touch it. However; you are locked into the company agreement with the custodian (e.g. Vanguard and their list of investment funds).
Not locked. You can roll it over into a IRA/ roth IRA and manage yourself. You won't pay early withdrawal taxes as long as you roll over within 60 days.
I have to believe that if a company is "managing" 401k investments, it's just an abstraction on top of some agreed-to investment strategy at the brokerage.