Is a Hollowtech II BB compatible with an Octalink Crank? (Shimano Claris) If I fit a Shimano Hollowtech II Bottom Bracket (Claris), can I still use my Octalink Claris crank?
No, you cannot, they are fundamentally different. Octalink uses a 3-piece crankset and Hollowtech 2 uses a 2-pice crankset.
The 3-piece means that the spindle is integrated in the Octalink BB. The 2-piece means that the spindle is integrated with the right crank and inserted through the hollow BB.
The BB is usually much cheaper than the crank so it is normal to buy the BB you need for your crankset if the crankset is OK. One only buys a different BB if their new crankset requires it.