Can I claim F1 student step child as dependent?

Try to make this short. Can my wife (permanent resident alien, aka green card holder) and I (US citizen) claim her children who are here in the US on F1 student visa's as dependents on our joint tax return?  They have lived here for over 3 years and we fully support them (room, board, tuition, etc.).

 

Or, if we are not able to claim them for the deduction, can we list them as dependents for other purposes (lower in-state college tuition, etc)?