i cant stress enogh how important it is to get the old paste off the walls before painting some pastes even turned the paint yellowish and crazed well spotted JOHND
lag the pipes just to rule out condensation on the pipes its cheap enough
dont forget get the ceiling done 1st then the walls to the last coat stage then pva your tiled area fit the kitchen leave kickboards off tile above worktops fit your flooring next then kickboards now fit your skirting...
im concerned it sounds like you dont seem to have any or much faith in the builders you are using (thats not good) have you seen there work ect
i am a kitchen and bathroom fitter 30 years served i have talked most people out of underfloor heating as its not that good most people like the idea...
mold wont die with anything like bleach ect it just takes the edge off it it in beds in the plaster there are so many reasons why we get mould if both walls in the picture are external then yes it may well be insulation thats caused it it could also be you need ventilation
really dont even try you will end up with a kitchen that looks like someone painted why not try painting the walls to change the look have look on google images at oak style kitchen cupboards and look at what other people have done you could also think about the changing the floor and blind and...
no handyman should be doing this he wont have the expensive and totally necessary equipment to do the vital checks electric can kill it really can i no you think this is not helping but really it is
ok im a fitter by trade i always get the walls to the stage where they ready for there last coat as for the tile area don't paint this get it as flat as you can now then before tiles pva mix then tile and finally your top coat on the painting ps the ceiling can be fully finished before you start...
with your spare bits practice wirewooling with a touch of bleach remember the top surface will only be a couple of mm thick
its easy to go to hard with sandpaper so try with wirewool also that oil looks fine i use danish oil but im sure that 1 will do fine