A popular proverb says, etc. Rashi intends to say that you should not ask how did the Israelites know that Hashem hated them. And therefore Rashi explains: Since they hated Hashem, they said that He also hated them, as a popular proverb says, etc.
What is in your heart regarding your friend, etc. I.e., whatever is in your heart — that you [subconsciously] hate your friend, you say about him — that he hates you.
[You imagine] is in his heart regarding yourself. I.e., whatever is in your friend's heart — that he loves you, you say about yourself — that you love him.
His taking us out was an act of hatred, etc. Rashi answers the question: From the verse it seems that Hashem took them out of Egypt because He hated them. But, He performed many miracles for them in order to take them out to freedom. Therefore Rashi explains that they said, "His taking us out [in itself] was an act of hatred, etc."
One of which was well-watered, and the other was dry, etc. Re"m writes: This is perplexing. Why does Rashi explain this verse as referring to a dry and a watered field? If it is to demonstrate that Hashem took the Jewish People out of Egypt because He hated them, the fact that He took them out to lead them into the hand of the Emorite and destroy them. is a greater proof of hatred. Re"m leaves this question unresolved. But it seems (to me) that Rashi is answering the following question: The verse should have said, "Because of Adonoy's hatred of us, He took us out [in order] to deliver us into the hand of the Emorite." Why is, "of the land of Egypt" needed? Rather, "He took us out of the land of Egypt," must be to make the comparison to the dry field and watered field. And the verse should be understood as: "For one, because of Adonoy's hatred of us etc.," — this is for the comparison to the dry field and watered field. "And furthermore, in order to put us, etc." The word בעל means a dry and arid land that requires irrigation.