Yep.
Probably. They won't accept any help at this point.
A bit late for that.
That's a lie, at least by omission.
The fact is, you broke our agreement and took Crete and likewise convinced Persia to break their agreement and take Miletus. That's a stab, plain and simple. I did what I had to do to break up a triple alliance between Persia, Egypt, and Rome. I went to you first, but you essentially blew me off when Spring 452 you didn't commit a single unit to fighting Persia. I had no choice but to help Persia. Fighting them would have been a stalemate at best because you were pouring troops at Carthrage and left your border almost completely undefended. I refuse to carry on this conversation any further until you explain to us all why it's my fault you left yourself wide open to Persia in Spring 452.
Let's assume that in 451 Persia and Greece were allied (which seems a reasonable assumption when Greece opens to Epirus and Dalmatia). Greece would go against Rome and Persia would go against Egypt (so, effectively Carthage, Greece and Persia sharing similar goals and working together for them (regardless of whether Carthage focuses on Rome, Egypt or both).
In this scenario, what should an Egyptian player do? If you are thinking about fostering distrust in the Greek-Persian relations, you are correct. And what would be the best way to do that? In my opinion it would be to persuade Greece that Egypt and Persia are working together. If Persia would go to Cyprus, everything would continue along decent tracks for Persia to attack Egypt next year, unhindered by any Greek forces.
Furthermore, a Persian fleet in Miletus is a Persian fleet that isn't threatening to go to Egyptian Sea in Spring 452. I vastly prefer to see that fleet there than in Cyprus, and similarly a fleet in Cyprus puts Egypt in a situation where that fleet's assistance is worth a lot to both sides. Conversely, a Greek fleet in Crete and a Persian fleet in Cyprus means that this alliance can move to Egyptian Sea with support (as they ended up doing) so we simply couldn't afford the risk.
Apart from that, our agreement, if memory doesn't fail me, was that I would cede Crete to Greece in return for assistance against Persia (otherwise, why make a deal just to let Greece have it for free?). When Greece moved all of it's armies against Rome, we considered that deal dead and buried because Greece clearly wasn't interested in fighting Persia.
As for why I "left myself wide open for Persia", I actually didn't leave myself open to any comparable extent as you did in 451. I had an army in Jerusalem and a fleet in the vicinity of Egyptian Sea, so exactly the same units that you had while facing Persia, only with quite a bit more ground to cover. I didn't expect Persia to get two builds that year because you just let them keep Miletus and gain Cyprus and Sinope, and if Persia didn't have those builds we would have been fine. We would also have been fine if you didn't go to Crete, which meant we would gain a build (though that is the most understandable of the lot and the one we did actually expect and were okay with.
Now, you PM'ed us after taking Crete and said "oh, so now that we have Crete we want the old agreement back, where you have your side of the pond and I have mine", so we thought that we were still kind of okay, as we still had a plan to delay the Persians until we could secure builds from Carthage to hold them back, but you killed it by supporting Persia to Egyptian Sea. So, that's three separate times where you acted to make the defense of Egypt almost impossible. I repeatedly told you that you were dead if I fell to the Persians but you ignored me.
Contrary to you, we had the same opportunity to support Persia to Aegean and kill off Greece, but we did not do so because that would just make life easier for Persia. In hindsight, perhaps that was the largest mistake - we would have been better off fighting Persia alone than fighting both Persia and Greece.
I did not ask to be friends or anything, but throwing away your winning chances (yes, despite your horrible start, Roman failures still gave you a chance after Persia moved out to attack me) just to punish Egypt for a perceived slight is incredibly petty. Oh, but you may ask, isn't that what you are doing to Carthage? Well, for a start, we only did it after losing all winning chances, which were predicated on Carthage forcing two disbands so we could get a build in Egypt. Without that build, there was no way to hold Egypt even if everyone else on the board supported us - and also we warned Carthage that this would happen if they did not went through with the deal.
TLDR: We would have accepted a NAP between Greece and Persia and even a stab against Rome as legitimate play, but actively helping Persia to attack Egypt in your current position is just playing to lose.