Yes, and yes, and also no? It's a complicated issue.

At first, when Greece and Ancient Egypt were two mostly distinct cultures, there was plenty of cross-cultural trade. Even as far back as the Minoans (1500 BCE) we've found Egyptian artefacts on Crete and seen Minoan pots in Egyptian tomb paintings. Clearly then, the cultures had a neighbouring influence on each other. But as Egypt had already been around for over 1000 years before the Minoans even figured out what they were all about, they represented a powerful influence over developing cultures.

One example of direct Egyptian to Greek cultural heritage comes in the form of the statues. The Greek statue we think of is quite life-like and fluid. However, in the earliest days of Greek statuary the forms are quite block-like and very stiff. This is a result of the Egyptian style essentially being co-opted into Greek art. You can even see the changes happen as the figures carved shift their weight from one leg in the Egyptian style, to both in the Greek style as time passes.

There are many more influences, but Alexander's invasion really stirred up the pot. With the Hellenic influence of the Macedonian Empire in Egypt, the tables had turned and it was the Egyptians turn to receive a lesson in Greek culture. The Greek lifestyle (having developed in the 1200 years since the Minoan Empire really took a turn) came back with a vengeance and it's here in Alexandrian and Ptolemaic (the successor to Alexandrian) Egypt that the cultures merge.

In Ptolemaic Egypt we get Greek customs and culture, like the gymnasia and theatre mixed in with native Egyptian customs. The languages also begin to mix, and it's here that we find artefacts like the Rosetta Stone which famously contained both Greek and Egyptian (in hieroglyphic and hieratic, or cursive, form) allowing scholars to decipher hieroglyphic Egyptian. The cultural melting pot of Egypt was so great that even the legal system in Alexandria allowed for Greeks to be governed by Greek law and Egyptians in native law, and when the Romans took over Latin and Roman law was added into the mix as well.

There's a LOT more on burial rituals and other artistic and linguistic influences (e.g. The form of modern native Egyptian today is Coptic, which is the native tongue written in the Greek alphabet with a few extra letters derived from hieroglyphics thanks to the Greek invasion) but I don't have the space to go into them here.

tl;dr - Alexander's invasion was like cultural exchange on steroids, but there was plenty of influence going both ways before that.

^^^edit: ^^^source: ^^^Can ^^^I ^^^claim ^^^my ^^^BA ^^^in ^^^Egyptology ^^^and ^^^MA ^^^in ^^^Ancient ^^^History ^^^as ^^^a ^^^source? ^^^I ^^^could ^^^try ^^^to ^^^find ^^^exact ^^^references ^^^but ^^^it's ^^^been ^^^a ^^^while.

Yes, but I think you'll find more influence from Greece's other neighbors, such as Persia and Phonecia, which had centuries of contact with Greece through the intermediary nature of the Greek cities on the Ionian coast of Asia Minor, both before and after Alexander.

However the Greeks/Macedonians who went on to rule Egypt after Alexander in the Ptolemaic dynasty became highly assimilated, to the point we forget Cleopatra was a Greek woman with a Greek name.