One meaning of "humanity" is (from Dictionary.com): "the quality of being humane; kindness; benevolence". So, I would say "full of humanity" is a fine expression (google search returns about 940k hits on it). But it's good mostly in writing. In speech, most people would use simpler phrases.

Humanity is a noun. It means the human race. Do you mean humility?

It's grammatically correct, but it sounds a bit weird in English. British and American English shy away from abstract terminology whenever it's possible (maybe you're likely to find a higher percentage of abstraction in Australian English). I think I would say "He's a very generous man" or something like that:) Sources: this is one of the main topics of an exam I'll be sitting in a month :)