What is the difference between genkikana and genkidesuka?

Question

I want to determine the difference between kana and desuka. I was able to translate them as "How are you." Thank you.

Answer 1

First, かな is a sentence-end particle that means "I wonder ...", "..., right?" or "I hope ...". In other words, ～かな questions are usually directed to yourself, although there can be a listener.

Asking someone else using かな is common when an adult asks a small kid.

• ○○ちゃんはいくつかな？
  How old are you, ○○-chan?
• ひとり？ パパかママはどこにいるのかな？
  Are you alone? Where is your mom or dad?

In Japanese, an adult tend to choose words from the viewpoint of the kid. Have you heard people use ママ/パパ instead of "I", 僕 instead of "you", and such? It's discussed here, here and here. So these ～かな questions are said as if the adult were at the kid's viewpoint.

Likewise, saying "元気かな?" directly to someone is acceptable basically only when you talk to a kid. Additionally, if you are far higher and older than the listener — say, if you are 60 and the listener is 20, you might use 元気かな without offending them.

But it's totally fine to say 元気かな referring to someone who is not present:

• 彼とはもう2年会ってない。元気かな。
  I haven't seen him for two years. I wonder if he's doing fine.

Answer 2

"Genki desuka" is a polite way of "Genki kana".

"-desuka" is keigo (敬語).