Your translation is very good, as always
Only a few minor corrections that have to do with the tricky words you keep asking about
Mai vreau decat o noapte sa iti arat ca te iubesc
I want only one more night to show you that I love you
Nu vreau decat sa-ntelegi ca imi lipsesti
I only want you to understand that I miss you
Sa stii ca imi doresc sa recuceresc inima ta
Know that I want to reconquer your heart
It's again the conjunctive case.
Să știi=
know that / I want you to know that
