As with all trees, a way to check for life is to remove a small portion of its bark - but not ringing the whole tree of its bark in the process as it will eventually dehydrate and die, which is one way to kill an undesirable tree.
Checking for growth is usually done on the trunk, but instead just check the "dead" limbs. If the limb is truly dead, there will be no green at the layer of the smooth core underneath and the appearance of the core will be creamy brown to deep brown with black veins.
The oak tree canopy is not on a one to one relationship with its roots. The preception that the "root ball" is a reflection below ground of the limbs and leaves above is not correct. An oak is similar to a wine or champaign glass with a wide base for stability and support and a canopy of limbs and leaves above.
The canopy is supported by an array of radially growing main roots for primary stability with support roots eminating from the mains. From the support roots are the millions and millions of hair-like (and infinitely smaller) feeder roots for capturing moisture and nutrients that are carried to the leaves for photosynthesis.
Fertilizing the feeder roots (not burning them) is always recommended. Fertilize at the drip line where the most active roots are growing.
I have oak trees that hurricane winds blew the tops out of, main trunks broken off in a whip-sawed fashion, exactly a green stick type of break, real ugly breaks. The trees survived that "catastrophy" and are regrowing limbs and lots of green leaves. My favorite tree stand is in one of these trees. Had I lost that tree I would be unable to see down a 300 yard lane through the forest as there is no other in that location. I want that tree to survive. I talk to that tree when I am on stand and feed it twice a year.
I see nothing wrong with trimming the dead branches from your oak. They are very hardy trees and will probably outlive us both.
