1. IMPORTAR-SE (reflexive = oneself) Meaning care (about), mind
Não ME importo DE DORMIR na casa (with a verb after, use preposition DE (or EM) = care about DOING something)
Não ME importo COM DINHEIRO (if a noun comes after use preposition COM = care about something)
Ele SE importa COM os amigos, He cares about (his) friends.
2. IMPORTAR - meaning have importance, be interesting
Não me importa dormir na sua casa = Sleeping in ur house is not important to me. (ME in this case = to me)
O dinheiro não ME importa. A saúde em primeiro lugar. (Money is not important to ME. Health comes first).
We can also say "O dinheiro não importa." (without pronoun ME) = Money is not important (to anyone, not only to me)