The Tiagra F derailleur is compatible with Shimano 8 speed road shifters. The Alivio is not.

9 Speed cranksets generally work fine with 7/8 speed chain. Alivo is a good crankset, though, and will work prefectly with your drivetrain. The tiagra deraileur is likely made for larger chainrings like the 48 and might be tough to get working perfectly (whichis necessary for use with indexed shifting.