It would seem the red, yellow, blue cable is cable to boiler, seems a little odd as both sets of contacts seem to be used, so I would want to test to be sure, however would expect to find blue = neutral, Red = permanent line, and yellow switched line.
The Hive uses a common back plate also used with other makes, there are three or four options
depending if single, two or three channel and if opentherm is used, I don't think Hive has the three channel or opentherm option, so with single channel you need a bridge wire line to 1 (Com) the other two are not volt free so not required, so it depends on which you select as to how wired.
The contacts are likely rated around 5 amp, so not suitable to power an immersion heater, one could use a relay, but can't see why one would want to.
Also can't see many central heating systems where there is a cylinder for domestic hot water not having a hot coil and some method to heat the domestic hot water from the boiler.
In my case we have C Plan and I can't stop the boiler heating DHW, I have the option of not running the pump so only DHW is heated, which was used, but is no longer used since solar panels fitted and the DHW in summer is heated when there is excess from solar panels. Autumn and Spring we can have a time when DHW is not heated, but not enough times to worry about.
Hive has a special function to work with C Plan, with separate outputs for boiler and pump. Not seen it with any other system, so you need to work out what you have. The odd way the existing unit is wired points to some failure in the past and some temporary rewire to get around the problem.
So for me the first thing is to work out how the existing is working. This
seems to be wiring for your boiler, not option for opentherm so likely Hive is best option, although I do see Ebus so maybe you need to look further it depends on how the ebus can be used, some boilers do offer their own analogue thermostat, but it may not connect to TRV heads, and the main thing today is to have each room independently controlled.
I see
@stem has beat me to it, he has far more knowledge to myself, so go by what he says.