>>17761141 (OP)>>Conquered the coastline of western Arabia (aka the Hejaz)This was actually planned
>Conquered CarthageHighly unlikely, they were the last major Mediterranean power other than Macedon by that point
>Conquered the rest of the Balkans and ItalyDefinitely not. Alexander had his heart rather set on conquering India and Central Asia. There really isn't that much to gain in the Balkans other than Thrace, which he already brow beat into submission. The Central Italians were incredibly militant and at this point they hardly had much of an economy, proto-currency wouldn't even emerge until they invaded Southern Italy which was just bronze bullion stamped in a circle by anybody who could. There is little for him in the West maybe other than Carthage and Syracuse, but why fight a naval war with the last major state in that part of the world when India is closer in logistics and has far more than just Sicily and Punic North Africa as an award.
>Would his empire survive with his heir ruling it?Stability in the Empire after his death continued for a couple years until his brother was assassinated and finally his son years after which was the real end of Empire. Presumably if Philip lived longer or his son was of age there is no reason not to think it would last. Though it's unlikely Alexander would have lasted much longer anyway, over the course of his campaigns he took 3 near-fatal injuries which for anybody would have needed major lifestyle changes and still have a massively reduced quality of life and caught a particularly bad strain of malaria. There's a pretty good chance he did just die of natural causes from his body failing