1:since half your gauge lights up its not going to be a fuse.check the individual light bulbs in the back of the cluster and behind the climate control.
2:I've always thought a stuck thermostat would make it run cold or not.not chirp like it does.I'm not too familiar with thermostats though.
3:mine does the same thing I throw it in neutral it chills at 1500 and when I stop fully it sits at about 1k-750.750 is norm for a dohc vtec.

skunk2racing97 will probably be in this thread shortly.he knows a hell of a lot more than I do about this stuff.

welcome to the honda community.