Upon exiting
Egypt the Israelites traveled to Mt. Sinai, which The Bible informs is in nothern Arabia, most likely in the eastern part of the land of Median, the country of Moses' father in law. From there they travel to the area around the Jordan River. Here they failed in faith and for forty years they wandered in the wilderness until God brought the remnant back to the promised land.
Yes, according to tradition, they traveled from Israel (Canaan) to Egypt in the time of Jacob (Genesis ch.45-6).
Israel
From Egypt to Israel it took the Israelites 40 years. It took this long because G-d wanted everyone of the slave generation to have deceased.
The Israelites were slaves in Egypt for roughly 400 years .
Moses led the Israelites OUT of Egypt. Joshua led them into the promised land (roughly where Israel is today).
They didn't. There are no records of any Israelites being in Egypt apart from the Old Testament. No Egyptian records or any other records mention them at all.
They lived in Israel before they were taken as slaves to Egypt.
The problem presented at the outset of the exodus from Egypt by Israel was their enslavement and oppression by the Egyptians. The Israelites were forced to work as slaves under harsh conditions, and they cried out to God for deliverance.
Because of famine (Genesis ch.42).
It was Abraham.The father of the Israel nation.
The Jews went to Israel, in Josephs time.
Because there was a famine in Israel and the only place to get food was in Egypt. They went to Egypt and instead of becoming citizens they were forced into slavery.
The Israelites' ancestors (Jacob/Israel and his sons and their families) moved to Egypt because of the famine in their land. See Genesis 46 (and the chapters before it) for the story.