Spousal beneficiaries can rollover an inherited IRA into their own IRA account. Non-spousal beneficiaries cannot. Non-spousal beneficiaries can either transfer the assets into an Inherited IRA or take a lump-sum distribution. Non-spousal owners of Inherited IRA's are subject to RMD's, but their exact options will depend on their situation. The IRA custodian can advise on this.
As Critter#2 said, once the Inherited IRA is established, the owner can determine how the funds are invested. Most IRA custodians offer a wide variety of investments. It shouldn't be necessary to change custodians in order to change how the funds are invested.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
