Best if you could provide a photo of the paint peeling off as there are multiple possible reasons that your paint peeled off, it can be skim coat too powdery causing adhesion problem or simply an inferior sealer was used.
I would recommend you to identify the root cause of the problem first before your painting job. powdery surface would require special solvent based sealer/water based (with specific function that tackle particular problem) sealer to be applied before finishing coat. If it is due to improper coating system or inferior grade products, then simply scrap off the old paint films and apply 1 coat of sealer + 2 coats of finishing.

1 litre can cover roughly 6-7m2, do take note that you need to x2 the amount for finishing as there will be 2 coats of finishing in a proper painting system.

imagine if you wanna stick something to the wall but you don't replace the old existing tape with a new one, the adhesion would be a big problem right? If you don't do the foundation right the problem gonna comeback no matter what as the base coat is already loosely attached to the wall.

From what I see in your photos these are bubbling issue caused by moisture in some walls. check if the skim is powdery or not, if not then high chance that it is caused by moisture issue. Scrapping off old paints are not that difficult, just get a scrapper from the hardware store and scrap those old paint films off.

As for the door, those are molds growing on the surface. The humidity can be quite high in the house. I would suggest you to check your wall moisture level before your painting works. Is this an old house that left empty for some times?