Not all pedals require this level of maintenance, but Speedplay is very specific in their owner's manual (that the shop should've given you, along with the product registration card) in regards to spindle maintenance as well as cleat lubrication (before every ride). All of this info and more is on their website as well.

As for Look/Shimano, they use a sealed bearing system that is maintenance free. My 1990-era Look pedals are still as smooth as the day they were made.
Replacing road cleats yes, they are only plastic. Metal SPD/Time cleats last forever.