Unless yours is a lemon, that's just the power rating. Bosch and most brands use 3.6/3.8KW, look for Pana/Joven/Centon high power models if you want very hot water.

Are you saying you switched from storage to instant heater? It will not be as hot, period.
You can reduce the input water flow to make it hotter, that's about it unless you want to hack and install a high-power model (yours is 3.6kW).

Gas

Very unlikely. Water tank usually installed on roof, natural pressure from gravity. Simple way to check is whether your sink tap got good flow or not.

You should just be able to unscrew the head and connect the heater input pipe if you want super simple. My plumber did it a bit neater, he removed the rain shower head pipe sticking out of the wall so my water heater connects directly to the pipe hidden behind the wall.

Your house no central pump but still got good water pressure on 1st floor? You can probably just get the non-pump version.

My old house used. Changed to storage dy.
Solar is convenient, but your electricity bill skyrockets during rainy season. For example, my area non-stop rain recently so anyone using solar would have to run electricity to heat the huge water tank (180L-300L is standard).
Also need to clean once a year to maintain efficiency and prevent moss. Either you clean yourself or hire people for a few hundred to come and clean. My old house was clay tile roof and they cracked when the workers climbed onto the roof to clean.
Basically solar is a nice option, but overall expensive and got some long-term concern. Would personally use gas/heat pump if I needed the capacity since I don't need to climb onto the roof then.

Never heard of such a thing before. I'd get a second opinion from another plumber, there should be zero problem if installed correctly.
Problem with instant water heater is that the heating capacity is generally not enough for rain shower.