Yes! You should always include all varieties of your keywords and in all match types. Even with the same keyword phrase I will ad all match types to it. I get different traffic numbers from all different types. As far as costs, you're going to be charged just like any other keyword. It's whatever you set your bid to. Hope that helps.
Hypothetically speaking, if I had a daily campaign with $10 - and:
granny smith ($2 per click) "granny smith" ($5 per click)
How would that end up spending my daily money? Is it down to previous clickthrough statistics, or does google choose to display the most number of clicks possible? Or does it base what to show based on conversions (using statistics where people have followed through to purchase Granny Smith apples).