[verb (plain)] + かな [i-adj] + かな [na-adj] + かな [noun] + かな [verb (volitional)] + かな
かな ends a sentence with "I wonder": the speaker is asking themselves, out loud or in their head. It goes after the plain form. A noun or a な-adjective drops だ before it, though past だった stays.
After the volitional form, かな turns the question onto your own next move: you are making up your mind, or announcing a decision softly.
These go beyond wondering to yourself.
Said to another person, かな asks without pressing for an answer. With ないかな or てもいいかな it turns into a soft request.
かな is casual. In polite speech the usual frame is かなとおもいます思います, or a question with でしょうか.