Cool. A Gunblade to go with the Buster Sword.

Skybreaker isn't exactly top-of-the-class, but I definitely think it is top-tier for a class of potential Sword Bearers (for +5 point cost). In order to get utility from this sword the key will be a high enough attack value so that the BCF attack hits and the followup ranged attack ALSO stands a reasonable chance of hitting. I wouldn't try to overthink potential combos to capitalize on the possibility of a ranged attack, focus instead on the chance of a followup. This Sword could be useful when playing tent-poles, or when you may be worried about having to grind through opponent's STOP clicks.

I could see using this on the SR SLOP 038 Apocalypse to get a second hit and using his P/PB for the follow up range attack.

With the Improved Targeting Adjacent, can a character use the ranged attack if the attack range is 0?

Unfortunately not. Skybreaker does not provide a minimum range or an exception to needing range and line of fire to make the range attack. With a range of 0, you can only see the square the attacking character is in.