Hi im new to this site, you are correct the Imm Heater should not be on a plug top nor should it be on a 13 amp double pole fused spur, it should be on a 20 amp doulbe pole unfused spure, the reason being is that under current regs the 13 amp double pole fused spure falls below the required protection, this is due to the current regs using the voltage range of 230V and not 240V calc this and you will come up with 2990 watts, and as you have stated the IMM heater is 3KW no diversity allowed 100%, and as for the shower pump is the plug top located out side the zones, if so then this would be ok acording to current regs, under a bath with a fixed panel screwd would also meet current regs, as this is clased as having to use a tool to gain access to under the bath, but must be fused acording to raiting of pump.
If not no cert can be issued for work, pump does not require one if out side zone on plug top. but IMM heater will.