How did Moses speak to the children of Israel & write the Torah if he was learned in all the ways of the Egyptians?

Moses’ mother, Jochebed was the daughter of a Levite, and she married Amram, another Levite (Exodus 2:1). The Hebrew midwives refused to participate in the infanticide decreed by the Pharaoh (Exodus 1:17–19). Moses’ mother Jochebed hid Moses in a basket of bulrushes and set him afloat on the Nile River to preserve his life (Exodus 2:3). Moses was raised as the son of Pharaoh’s daughter. Jochebed became Moses’ nurse and was paid by the king for her service (Exodus 2:7–9).

This was no accident or coincidence. It was as a result of God's divine will.

As Moses grew into adulthood, he began to empathize with the plight of his people, and upon witnessing an Egyptian beating a Hebrew slave, Moses intervened and killed the Egyptian. In another incident, Moses attempted to intervene in a dispute between two Hebrews, but one of the Hebrews rebuked Moses and sarcastically commented, “Are you going to kill me as you did the Egyptian?” (Exodus 2:14). Realizing that his criminal act was made known, Moses fled to the land of Midian where he again intervened—this time rescuing the daughters of Jethro from some bandits. In gratitude, Jethro granted his daughter Zipporah to Moses in marriage (Exodus 2:15–21). Jethro is described as “a priest of Midian.” He is also referred to as Reuel (verse 18) which means “friend of God.” The fact that the Bible calls him first by this name may mean that he was a priest of the Most High God, rather than a pagan deity as some have suggested.

Moses encountered God at the burning bush (Exodus 3—4), where God called Moses to be the saviour of His people. Despite his initial excuses and outright request that God send someone else, Moses agreed to obey God. God promised to send Aaron, Moses’ brother, along with him. Along with Moses and Miriam, Jochebed had at least one other child, Moses’ brother Aaron (Exodus 6:20).

Why did God select Moses to deal with the pharaoh? For the very reason that Moses was learned in the Egyptian ways and in its religion. This was no hindrance – in fact, it was essential that God’s representative was in a position to understand the ways of the Pharaoh and know how to address him. Can you imagine a Hebrew slave being granted admission into the royal presence?

How did Moses speak to the children of Israel & write the Torah if he was learned in all the ways of the Egyptians?

With regard to understanding the Hebrew people, their language, their history and religion, Moses was brought up in the house of his mother, who nursed him for several years (Exodus 2:7-9).

With regard to language and the ability to speak with the Hebrews, Moses was an educated man. Also, as a grown man he was in contact with the Hebrew slaves and was perfectly able to speak with them and to understand them (Exodus 2:14).

With regard to writing the first five books of the Hebrew Scriptures, never overlook the fact that it was God who chose Moses. It was written under divine inspiration. Also, those first five books were written over a long period of time and it was customary for a scribe to handwrite words dictated:

The Torah was written approximately 1400 BC. Traditionally, the Torah is handwritten on a scroll by a “sofer” (scribe). This type of document is called a “Sefer Torah.” A modern printing of the Torah in book form is called a “Chumash” (related to the Hebrew word for the number 5). https://www.gotquestions.org/what-is-the-Torah.html

Let me give the simple answer.

"Learned in the ways of the Egyptians" does not imply that he wasn't also learned in the ways of his own people as well. Many Egyptians would have known the language of the Hebrews, and there is no reason he wouldn't have learned it. It's also likely that some of the Hebrews knew Egyptian. As for writing the Torah, he had many decades between visiting his people at age forty and writing the Torah.