Lack of Hot water pressure

Probably have trash in the stem. Turn off water to hot side remove handle and stem look for debris. If none visible cup your hand over the the hole where the stem was so the water will flow to the sink drain. Then slowly turn water on. If water really comes out then stem may be clogged. It'll make a mess so have a towel or 2 handy

Could be the diaphram in the water section not working or a blockage in the water section ie lack of water pressure to open gas .

This is dependant on the manner in which your unit is installed. In a normal system, there is nothing that would cause this except debris in the water line. If you have a water heater that is a tankless variety or other supplemental connected systems, you will have to reset those due to lack of water pressure tripping a safety feature to prevent overheating.

Hi Fran:
Most shower faucets now are equipped with flow restrictors. It is possible with some units to remove the flow restrictor plate from the shower nozzle. It has to be dis-assembled to do that.
Regarding the lack of hot water, that would usually be a different problem and will be related to the hot water source.
Hope this helps.

when installing a new cartridge it is nessesary to put stem grease on the o-rings or you are taking a chace of cutting the o-ring which will cause the coldwater to mix with the hot causing the lack of hot water this is a very common problem but easily preventable with a little grease

over heating possible bad gas control valve , relief valve bad or water pressure too high or overheating will cause it to leak also lack of thermal expansion tank

Could be thermocouple.
Might also be lack of air supply, or low gas pressure, or bad gas control valve, or tripped FV system due to lack of air supply:
http://waterheatertimer.org/How-to-test-water-heater-thermocouple.html
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

If your house was built before the "70's the most common reason is that the hot water trunk line to you shower has corroded shut to the point of reduced flow. It is not uncommon for this to happen on just one line. The controler its self could have an obstruction on the hot side. Replacing the internal part(s) should take care if this. Try to identify the brand of controler and research available part(s).

You have a water valve, which controls the hot & cool water. It appears that your hot water side leaking in to the machine while machine is Idel. Can pull valve make sure nothing is in it causing to leak or replace.

Try replacing the thermostat, it sounds like a lack of water circulaton.

Ed