I don't know enough to answer (A), but with (B), the Byzantines would probably be able to bring their Italian war to a close sooner, and to hold onto the peninsula after it's conquered. This in turn would greatly boost the Empire's strategic depth against enemies from the east, in particular the Sassanids and Arabs. Seeing this, the Persians might not attack the Empire in 602, or if they do the Byzantines might not come so close to collapse, meaning that the war follows the usual pattern of a few sieges and battles in Syria/northern Mesopotamia followed by a compromise peace, rather than being the quarter-century slug-fest it ended up being. Accordingly when the Islamic caliphate starts trying to expand out of Arabia neither the Byzantines nor the Sassanids would be anywhere near as exhausted as OTL, meaning that they'd probably be able to defeat any invasion from Arabia. It's difficult to say what would happen after this, because the butterflies would be so huge.