let's bring a closer look at the structure:
subject: filibuster( a device =>singular)
main verb: seems
The filibuster, a device that slows .... and tests..., seems more and more an anachronism in the age of telecommunications.
(B) sessions and tests the endurance of everyone who is associated with it, seeming to be
© sessions, tests the endurance of everyone associated with it, seems ( lack of and)
(D) sessions, that tests the endurance of everyone associated with it and seems
A it is
(E) sessions, testing the endurance of everyone associated with it and seeming ( no main veb)