The Ptolemies will probably be overthrown by the Seleucids without Roman assistance
This is very likely. Even the famed victory at Raphia was just sufficient to keep the Seleucids from invading Egypt. But Ptolemy could do nothing at all, even when Antiochus went east to gather allies and treasure. In fact, the Parthians and the Graeco-Bactrian kingdom acknowledged Seleucid supremacy when Antiochus came calling.
and the Seleucids themselves have to worry about the Parthians and Armenians further down the line.
Possibly. It depends on how the Graeco Bactrian kingdom fares. IOTL, it fell to the Parthians, who then gathered enough power to successfully go to war with a Seleucid kingdom weakened by the conflict with Rome. But if the Seleucids are strong, neither Parthia, nor Pergamum may become as powerful as IOTL.
One can imagine Anatolia being unified by either Pergamon or Pontus, or maybe even reconquered by Macedonia. Macedonia remains to be the most powerful state in the Balkans until the Dacians unify, which could lead to a very interesting conflict.
Under Antiochus III, Anatolia had been almost unified by the Seleucids. Pergamum, Pontus and Armenia were all mostly subservient to the Seleucids. It depends on how the Seleucids manage their myriad conflicts. But remember - they have two major advantages ITTL, that they did not have IOTL.
a) The Egyptians are toast. So - they have the resources of Egypt (but Egypt is as much an asset as a liability, given its propensity for rebellions) for any conflict in Anatolia. Also, with Egypt and the Levant in their hands, they have a first class navy, which is vital for conflicts in Anatolia.
b) The Parthians and the Armenians (and later, Jews) were all successful in conflicts with the Seleucids after the battle of Magnesia, where the Seleucid kingdom was irrevocably ruined. But ITTL, there is no Magnesia. The Seleucid kingdom has its full strength for any conflicts. In fact, they could become a very powerful kingdom that rules all of Persia, Mesopotamia, Syria, Egypt and Anatolia, if they play their cards right. Sure, the Parthians, Armenians, Pontics, and even the Pergamese are pains, but they may not have the strength to inflicts a fatal blow to the Seleucids as IOTL. In fact, the Jewish revolt is going to butterflied away. The revolt began because the Seleucids taxed the region excessively to pay the reparations imposed on them by Rome.
Rome probably won't expand anymore in the foreseeable future. This was their big break into Empire (as in a land ruling other lands, not as in they had an Emperor), and maybe Rome collapses in Italy after a Social War analogue. Gauls may continue to invade later on, and the Illyrians will continue to pirate the Adriatic until someone (possibly Macedonia?) pacifies them.
The thing is - Rome has a need to import grain from Egypt. As long as the Carthaginians don't seal off the straits of Messina, and the Roman grain trade continues uninterrupted, they may be content to leave Sicily in the hands of Carthage. If Rome loses in the first Punic war, and even the kingdom of Hiero is taken by Carthage, the island will be fully in the hands of Carthage, with no real source of resistance to them. However, Rome will still control the Italian peninsula, probably right up to the Alps, particularly if the Gauls invade unsuccessfully (and I really cannot see the Romans losing at this point to a Gaulish invasion).
If the Romans play their cards right, they can pacify their south Italian allies with lands taken from the Gauls, and there may be no Social War. The problem IOTL was how much Rome had levied from them, in comparison to what they had got from the conquests. But ITTL, Rome has taken far less from them, is far less powerful, and will, consequently, have to be much more diplomatic, and more cognisant of the interests of its Italian allies.
The big question is, with Carthage continuing to control Sicily, Sardinia, and Corsica, will they have the incentive to conquer Spain like OTL? The main reason they did this was to exploit the silver there to pay back the Roman indemnities and to compensate for the loss of Sicily. They could, over time, absorb Numidia, but I'm inclined to say it is more likely that the Numidians invade Carthage, and take control of the area themselves by the 1st century AD (for the record Christianity would probably be butterflied away), similarly to how Germanic tribes would later invade Rome.
While I can easily see Carthage having no interest in conquering all of Spain, I can see them taking control of the Greek trading cities of the Hispanian and Gaullish coast. Which means that Emporia, Narbo, and Massilia could all become Carthaginian. Even if Spain is not conquered, it would end up becoming a Carthage influenced region. Maybe even Gaul and Britain will have a lot more Carthaginian influence ITTL.
As for Christianity, an analogue could easily arise. Christianity was the religion of the poor in the early Roman empire (which is why Celsus contemptuously calls it the `the belief of the whores, slaves, beggars and thieves'). I am not sure if the Greek propensity for slavery was any less than the Roman one. Greek slavery will likely provoke a Christian analogue, where the poor look for a saviour.