Wonders and Signs

What wonders and signs were shown in "Egypt" (Acts 7:36)?
Egypt was hit by the following ten plagues: (1) all bodies of water in Egypt turned into blood; (2) frogs covered Egypt: (3) lice covered Egypt; (4) swarms of flies covered Egypt; (5) all livestock of Egyptians that had been out in the open field died; (6) boils broke out on all Egyptians and their remaining animals; (7) hail decimated all of Egypt except Goshen where the Jews lived; (8) locusts ate all plants in Egypt; (9) total darkness covered Egypt except inside the homes of the Jews; (10) all firstborn Egyptians and the firstborn among their remaining livestock died (see Exodus 7:14-12:30).

What wonders and signs were shown "in the Red Sea" (Acts 7:36)?
When the Egyptian army chased after the Jews after they left Egypt, God blocked the Egyptians, parted the Red Sea, let the Jews cross it on foot, and then drowned the Egyptians when they tried to cross it in pursuit of the Jews (see Exodus 14:5-31).

What wonders and signs were shown "in the wilderness" (Acts 7:36)?
God fed and clothed an entire nation of people for "forty years" (Acts 7:36), including with bread from heaven and water from rock (see Exodus 15:22-17:7). 

When did Moses say "to the children of Israel, The Lord your God will raise up for you a Prophet like me from your brethren. Him you shall hear" (Acts 7:37)?
In Deuteronomy 18:15: "The LORD your God will raise up for you a Prophet like me from your midst, from your brethren. Him you shall hear."

Why are the first three uses of the second person pronoun singular ("you/your") in Deuteronomy 18:15 but plural ("you/your") in Acts 7:37?
When Moses prophesied to the Jews in Deuteronomy, he used both singular and plural second person pronouns to address the nation of Israel and its people. In Acts 7:37, Stephen paraphrased in plural for the "children of Israel" what Moses had prophesied to the nation (singular) of Israel.

How do we respond to the cults and religions that refer to this verse to legitimize their leader?
Simply continue to read: "And it shall be that whoever will not hear My words, which He speaks in My name, I will require it of him. But the prophet who presumes to speak a word in My name, which I have not commanded him to speak, or who speaks in the name of other gods, that prophet shall die.’ And if you say in your heart, ‘How shall we know the word which the LORD has not spoken?’ - when a prophet speaks in the name of the LORD, if the thing does not happen or come to pass, that is the thing which the LORD has not spoken; the prophet has spoken it presumptuously; you shall not be afraid of him" (Deuteronomy 18:19-22). Notice that a prophecy coming true does not automatically qualify the person as a prophet of God, since those possessed by Satan can also foretell the future to a limited extent through demonic - not Godly - powers, hence the proliferation of fortune tellers. But a prophecy that does not come true, as is the case for those uttered by the leaders of cults and the other religions, automatically disqualifies the speaker as a prophet of God.

What "living oracles" (Acts 7:38) did Moses receive to give to Israel?
See Ten Commandments.

When did Israelites turn their hearts "back to Egypt" (Acts 7:39)?
Constantly, at the Red Sea, in the wilderness, at the base of Mount Sinai, even in the Promised Land, whenever things became a bit uncomfortable, the Israelites complained and talked about how good things had been in Egypt, which was untrue.

What "calf" did they make "in those days" (Acts 7:41)?
See Exodus 32.