Will placing live rock from the LFS in the tank start the cyclying process? The live rock from the LFS is partially to fully cured. The water is 78deg with sg at 1.024. Do you add live sand before or after the cycling is complete?
Yes the rock and sand will both help kick off the cycle. I would figure out your rock layout then add the sand after you get it arranged if you're planning to keep any bottom dwelling diggers.
Add the sand now. The severity of the cycle will depend on the status of the rock. Typically moving fully cured rock from your LFS to your tank will cause some die off but if the rock was kept submerged, the die off will be less than wrapping it in newspaper/plastic.
If you trust what your LFS said about the rock being cured then don't force a cycle if you don't see spikes. Just let your parameters settle down and slowly stock the tank.