Hot watwer leaks from the hot side of the facet

If the release valve referred to is the pressure release valve, then a water leak out the attached vent pipe is an indication that the valve is failing. To change the valve, the water must be allowed to cool (turn off AC power or gas) and the water level inside the tank must be lowered (drained) to below the level of the pressure relief valve. Once this is accomplished the vent pipe is unscrewed from the relief valve and the pressure relief valve is unscrewed from the water tank. A new pressure relief valve with a sealant on the threads, is then screwed and tightened into place with the outlet port facing downward. The vent pipe is attached to the new valve and the tank refilled with water. A hot water facet must be opened to allow air to exit while filling. Upon becoming full (water will begin to flow from facet), turn off the facet and restore AC power or gas, therefore allowing the water heater to heat up. When the first hot water is utilized there may be some air expelled from the facet.

the possible cartridges you can replace are listed on this pdf
http://www.deltafaucet.com/media/SpecSheet/DSP-B-R18000_Rev_A.pdf

Make sure that the valve under the sink is fully opened.

id say your tub spout or shower pipe is leaking and running down behind remove both and replace teflon tape see if it stops

It appears some scale from the water heater has the valve obstructed. Going to need disassembly to clear it.

Switch the line to the hot water facet and turn down thwe thermostat in the unit.

Sounds like you have hard water.  You need to change the inside of the facet.  before doing anything make sure you CAN get the parts for you facet.   Danze are not very expencive you might just get a new facet.  If this is a hard water problem you might want to buy a moen facet with a life time warrinty.  More money but free replacement parts.

There is something in the line or in the faucet.Are your pipes going to the faucet black iron or galvinze.Some of the pipe will rust up and stop a full flow of water.But I would check the faucet first to see if the screw is loose or somethng in it.

Is this single handle?If so, you need a allen wrench to take handle okk.But come to think about it you get the tools with the repair kit.