Are these correct and natural?
My leg hurts me. (Now)
I have a pain in my leg.
My leg pains
Or what’s the best way to express this?

Question

Answer

My leg hurts./I have a pain in my leg/I have an ache in my leg./My leg is sore. /My leg hurts/ My leg smarts./My leg aches.

Answer

If the pain has been ongoing or bothering you for some time, you could say, 
 "I have been having pain in my leg" or "My leg has been hurting me".
The word, pain, might sound more extreme than the word, hurt.
For example, saying, "I have a pain in my leg" sounds more serious than, "My leg is hurting me".

Hope this helps

Answer

My leg hurts    or     I have a pain in my leg.   Either one sounds natural in American English.

Answer

Crying.