Yes and no... solid state have much less impact on sound and should be pretty neutral for the most part unless the manufacturer intentionally made adjustments to tune them in a specific way..
Tube amps, on the other hand, can be extremely clean and neutral or can add color and warmth. This all comes down to what the user wants, the setup, and tubes used.
No. Swimmers ear is caused because the ear is influenced by outside water constantly entering the ear canal and not draining, not natural sweat and ear wax the body produces. Your body is not going to produce enough moisture to cause swimmers' ear because of over the ear headphones.