[SETI20]

high idle is a common problem.
You could try cleaning out the EACV. It's on the back of the intake with 2 bolts. Pop it off....easy job. Don't spill too much coolant tho.

There's also a control screw on the throttle body. Flat head, copper colored. Try adjusting it a bit.

The RPM's dropping sounds like your alternator needs refurbishing.
It's a messy job, but not hard and relatively cheap too.

 

[SETI20]

Any decent shop familiar with honda parts can get you a refurbishment kit.

And, the main relay has nothing to do with idle. It only controls the fuel.