What could cause the loss of hot water pressure in sink and shower but works fine everywhere else in the house

You have a blockage on the hot water inlet to your shower valve . If all other hot oulets are fine . Take the valve out and check the mixer body for blockage . Or do you have a valve on the hot side that is not fully on .

the common cause of that is you have higher water pressure at your sink tap..and have lower water pressure at your shower.. because your using a multi-point type water heater..it requires 2.0 ltrs/min..
you do this...try to open your shower together with your sink tap faucet.

It's doubtful your water heater unit is the problem. There is simply no reason for it to only work on sinks unless some how the pipe size was drastically reduced coming out of the unit so sinks got plenty of hot water but the shower does not. Take a second look at the installation. The pipe should not be less than 1/2" coming out. If that's OK then consider a clog or valve problem.

If you are using water in another part of the house most times the pressure at the bathroom shower will go low. For instance if some one in the kitchen draws water in the kitchen sink this will make the shower water even turn cooler because of low pressure. Flushing the toilet will also do the same.
Most houses are plumbed with half inch water pipe and would work a lot better if it was three quarter inch to give more water pressure.

Cold water pressure is what give you your hot water pressure so they should be equal but if you have a restriction on the hot side such as a valve not opening on the hot side or not opening all the way then you will have less pressure or the pipe work on the hot side is not proper. Hard to say but check the valve on top of the hot water heater

Something is clogged - take them all out and snake them out.

Screw off shower head-obstruction in water saver disc or screen,piece of rubber or rust

As you look at your valve on the right you will see a large screw fitting.inside this fitting is a temp/ pressure balance spool. it has failed for some reason and needs to be replaced. On both sides of the valve are 2 smaller screws. these are the water shut off valves. turn off the water and remove the larger screw fitting. remove spool and replace. Hope this helps.