[verb (plain)] + かしら [i-adj] + かしら [na-adj] + かしら [noun] + かしら
かしら goes at the end of a sentence and means "I wonder": you are asking yourself, or thinking aloud, rather than putting a question to someone. A verb or an い-adjective comes before it in the plain form, and a noun or a な-adjective takes it directly, with no だ.
In the past, だ comes back as だった: だいじょうぶ大丈夫だったかしら. In the present it drops out.
These go beyond wondering aloud.
After a negative request – きごう〜てくれない, きごう〜てもらえない – かしら turns the wondering into a gentle request.
かしら can also follow the polite form, which gives a refined, rather formal question.