He: 0.33 atm
O2: 0.52 atm
Partial pressure of a gas in a container is independent of and not affected by other gases present. Each gas will diffuse and occupy the full volume of the container. When calculating the partial pressure of one gas, other gases may be ignored at the moment.
Using the ideal gas law, when volume is doubled from 200ml to 400ml, pressure halves. Thus, partial pressure of He in this container is 0.33atm.
(Ideal gas equation: pV=nRT)
The volume of O2 initially is the same as the final volume of O2. There is no change in the partial pressure of O2.