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If the problem is only in the tub/shower then the culprit is the tub/shower valve (or maybe the piping to it) not the water heater. If the tub/shower valve/faucet has only 1 handle then it's likely that the cartridge in the valve (the working mechanism) is the culprit. The cartridge can be replaced if the valve model and brand can be identified. As far as water flow is concerned the tankless will only fire up if there is adequate water flow. This is usually around 1/2 gallon a minute. So very low flow won't turn on the heater.
You should have the tankless flushed with a mild acid solution every year or 2 depending on your water conditions. If you have town water from a reservoir you can go a couple years. If you hve a well or the town gets its water from a well flushing it every year is a good idea. This is probably a job best left to a plumber.