The phrase you're looking for is actually "open-minded".  When one is open-minded, they're willing to listen to other opinions and, if properly convinced, change their beliefs.  The opposite of this would be closed-minded, like when you enter into a discussion with someone and they refuse to hear anything you have to say or change their mind.

"Open-hearted" would be more like someone who is very generous and caring, and is always there to give a helping hand.  

Definitions for each: 

Open-hearted:


  
  kindly and warm
  disclosing intentions and thoughts clearly; candid
  


Open-minded:


  Receptive to new and different ideas or the opinions of others. See Synonyms at broad-minded.


What's the name of the characteristic of being "open hearted"?
The OALD says that ages is, "informal, especially BrE."

Is ages as in "I waited for ages" only used in British English?
If it is also used in other English dialects, is there any difference between the usage in those dialects? For example, is ages considered informal in one dialect, but not in another one?
