To add a gloss to the excellent answers offered by members of our community of wordsmiths, I propose to offer the word moonstruck which seems to cover the OP's request for a luna reference to the Portuguese expression.
moonstruck (Merriam-Webster): affected by or as if by the moon: as
a: mentally unbalanced
b: romantically sentimental
c: lost in fantasy or reverie
Note: As an additional answer for the OP's consideration, I offer the words lunatic and lunacy.
From M-W's definition of moonstruck one might infer that such a person is likely to exhibit mood behavioral patterns of the type the OP characterizes as "unstable and [changeable] at random". The M-W's definition of moonstruck enables us to link the OP's reference to moon and then cross-reference it to the word lunatic which Wikipedia informs us is an "informal term referring to a person who is considered mentally ill, dangerous, foolish or unpredictable (my emphasis), conditions once attributable to lunacy...[which] derives from [Latin] lunaticus meaning 'of the moon' or moonstruck (my emphasis)".