かな

1. 1Expresses wondering or self-directed doubt, often with a question word: "I wonder …".Ex. 1
2. 2Voices uncertainty about a quality or state as a musing, often half-addressed to the listener as a soft question.Ex. 2
3. 3With a negative verb (〜ないかな), expresses a wish that something would happen: "I wish … would …".

Casual spoken particle, used when musing to oneself or softly sharing a doubt with friends and family. It sounds tentative and self-directed rather than like a direct question, so listeners may answer or simply let it pass. In polite speech, でしょうか is used instead.

• かしらN4「かしら」 has essentially the same meaning and attachment as 「かな」, and both its musing-to-oneself use and its hopeful/requesting 「〜ないかしら」 form are interchangeable with 「かな」. It does, however, carry a traditionally feminine nuance that men generally avoid, so 「かな」 is the safer choice for a neutral tone.
• だろうN5「だろう」 also expresses conjecture, but with more confidence and a weaker questioning feel than 「かな」, and with rising intonation it asks the listener for confirmation. Its register is neutral, so it works in writing and news, but it lacks 「かな」's senses of hoping or making a soft request.
• でしょうN5「でしょう」 expresses conjecture with fairly high confidence in a polite, neutral tone, usually addressed to the listener; with rising intonation it seeks confirmation ('..., right?'). 「かな」 carries less confidence and a stronger questioning feel, is mostly muttered to oneself in a casual register, and also has hoping and requesting uses.
• ないものかN1「ないものか」 corresponds only to the hoping/requesting uses of 「ないかな」 and 「てくれないかな」. It leans literary, is typically used for things unlikely to come true with a stronger, more anxious longing, and often pairs with 「何とか」; it never expresses plain questions or conjecture.
• といい / たらいいN4「といい」 and 「たらいい」 overlap with 「かな」 only in expressing hope. 「かな」 uses 「〜ないかな」 with a musing-to-oneself tone and is limited to speech, while 「といい」 and 「たらいい」 are register-neutral, can take 「のに」 to express regret, and also serve for wishes, suggestions, and asking how to do something.

かしら has the same wondering meaning with a traditionally feminine, softer tone. だろう and でしょう mainly express conjecture but can also voice wondering, as in どうだろう or どうでしょう, with だろう sounding plainer and more reflective and でしょう polite, whereas かな is casual and personal. ないものか is a literary, earnest wish, and といい / たらいい state a hope directly, whereas 〜ないかな voices it casually and indirectly.