I hate doing this point by point posting anymore, but I'm wanting to address each of these individually...
Well , it depends on the POD. Assuming that there is a butterfly net around Arabia ,it is safe to say that Heraclius would still defeat the Sassanids in the same manner and degree. Two options would emerge:
1: Within a generation or two , another great Shah rises to power and repeats the process all over again.
This is, I think, a very plausible thing to happen. If not a new Sassanid shah, perhaps a dynastic change or invasion off the steppe, leading to a new Parthian-like Iranian Empire. Another round of decentralization could leave Iran weakened (but not to the point of easily losing) in the face of a resurgent Eastern Roman Empiire, leading to at least a bit more peace, or at least security, in the Levant and eastern Anatolia.
2: Arab Explosion. Persia dissolves into Anarchy , Mespotamia is conquered, Byzantines forced to accept Arabs into the Levant , though they might still hold it .
It really bears mentioning that the Arabs were
already in the Levant. The Muslim conquests over-ran a Syria and Palestine that were largely already Arabicized, Arabic-speaking, and Christian, or at least Jewish. One of the reasons the Muslims were so successful is because of the proto-Arab nationalism that was a part of the very early (pre-Abbasid) Islamic method of government. If migration out of Arabia continues to be by individual tribes and people, this process will continue and Mesopotamia will likely end up Arabic speaking, too, anyway.
3: Persia collapses. Turkic invaders and local lords slug it out. Romans with frontiers on Zargos and Tigris. Provided that they get a string of competent Emperors, they should be able to hold on to Italy and perhaps in the next few centries resubjagate Hispania. If some Hegemon maintains control over modern Germany and France , ala Charlemange, and that dynasty holds, Byzantine expansion northwards would probably be checked.
I think resubjugating Italy might be higher on the priority list: Remember, by the time of Heraklios, the only parts of Italy still held were what would one day become the Pentopolis, parts of Southern Italy outside the Duchy of Benevento, and areas of Nothern Italy like Genoa. The rest is held by Lombards. North Africa is still held relatively tightly (Heraklios starts out as an Exarch there!), so the re-taking of the rest of Italy is only a matter of time, but it still must be done before any dreams of re-taking the Iberian penninsula, let alone Francia/Gaul. Once that is done, then they can start pushing west from Carthage, take the rest of North Africa, then push back into Hispania.