Is it possible to get energy from frozen methane without oxygen?
The planet will have gaseous oxygen if it does have an atmosphere, and if that is the case then with enough energy(like a spark) atomized hydrocarbons could be lit for energy. What is atomizing you say? Well its just breaking a liquid apart into little particles, making it easier for the oxygen to react with said methane.

As for recycling the oxygen from the combustion reaction, it will not be possible to do in an energy efficient way, CO2 is too stable and the bonds are too strong.