Mimosa are a weed here and are just as comfortable in a standard potting mix as to peat/sand or clay, so I doubt they care, they also infest many crops here, so fertiliser seems to have very little negative effect on them, if any, I cant say for sure (as I don't live in your climate) but I would imagine a shallow water tray, tap water should be fine and potting mix you have spare, they seem to colonise gravely clay faster here, so maybe a wet open mix.