The 'bottom leaves' are actually cotyledons, which contain stored food for the seedling. They eventually always turn yellow and are no longer needed, as the food is used to support new growth. Typically they will be lost after at least a couple weeks, but if the medium lacks nutrients it will be sooner.
The soil 'broke' when you were transplanting because the root system had hardly developed and thus no roots were there to hold it to the shape of the container. That seedling should have been left alone to develop a more pronounced root system and a few more sets of true leaves before you considered transplanting it at all. If you transplanted the mass of unrooted soil directly into the perlite, then over watering could be exacerbating your problems indeed. There wouldn't really be any roots there to absorb the majority of the water you are providing, so your result is a sopping wet ball of soil surrounded by perlite.