What are these protruding things on this Russian military aircraft (MiG-31BM)?
The upper thing is a mirror for the WSO's (rear seater's) periscope.  It gives that position some forward visibility when extended.  Without it, I doubt that position could see the runway.  There are several other Russian aircraft with periscopes.
The lower ones are speedbrakes.
Looking at the underside of the vehicle my speculation is that they interfere with the landing gear retraction, so are extended until that point.  But if that's true, do they have to extend when the gear come down for landing?  No idea.  I can't think of another good reason for them to be open on takeoff.
A comment from ymb1 showed a very nice image of the doors/speedbrakes on wikimedia 
This shows that they need to be extended until the gear is retracted.