It is basically meaningless(or ignorable) or playful form.
But sometimes can have trivial meanings.
할까나 ca be used in various situations.
When speaker pretty sure or (partially) agree with specific fact or opinion. Or speaker is not sure about the matter or fact.
The speaker is aware of the topic, but he or she wants to deliberately pretend to be ignorant on the matter. (Though listener knows exact fact or their opinion)
The common concept of the ㄹ할까나 is what speaker wants to say is not the fact or matter itself but opinion (sometimes it implies asking for listener's opinion, not objection) with intention of avoiding criticism or objections.
—랄까나 is too.(~라고 할까나)
This is really tricky to a foreigner. Also, it is not a standard form of Korean. As I know, it is not listed on Korean dictionary.
It can be understood as irresponsible. So need to be avoided on public. Many Koreans use this word only in SNS or with friends.
It is prediction form with asking
오늘 비가 올려나? → It might be rain today.(?)
까나?are different. For the former the closest meaning in English I can think of is
그럴까나, 아니면 저럴까나...And
까나?is used when teasing someone.