1. Visible or not is not a key point. We say "遠くて見えない It's far, so I can't see it." and "富士山を遥かに望む I overlook Mt. Fuji far./ Mt. Fuji is overlooked far." 2. 遠い is an i-adjective and遥か is a stem of na-adjective遥かな or an adverb. 遥かな is different from usual na-adjectives. Only 遥かな and 遥かに are used. 3. You wrote"「遥か」is further away than「遠い」". I agree with you. I feel 遥かな未来<みらい>（the far-off future）is further away than 遠い未来（the far future）. 4. We can say "富士山を遥か遠くに眺めるI look at Mount Fuji far in the distance". It's a usage of a stem of na-adjective or an adverb. 5. 遥かに is used as "much more". こっちのほうが遥かに大きい／遠い／近いThis one is much bigger/ further /nearer.

「遠い｣は単に「遠い」ことを表したい時に使います。 「遥か遠い」は、見える、見えないにかかわら、「ずーっと遠いこと」を強調したい時に使います。