Re: horsehair plaster over brick!... (+) crystals & crumbling
The efflorescence is deposited as the water which bears soluble minerals and salts evaporates as it reaches the dryer basement air; the minerals/salts do not evaporate and are left behind as a deposit. A lot of the white crystals is from the mortar between your foundation masonry. The groundwater is dissolving it, over time that becomes very serious. It's not a large amount of water all at once, but it is a small amount of water in motion all the time. The matter has to be addressed from the outside of the basement. Drainage, pointing of the foundation walls, and maybe some sealing and membrane to exclude water.
Remove not the ancient landmark, which your fathers have set.