What is the ruling on saying: "Do not swear by Allah" to someone who has sworn by his father's mercy more than once, and does that necessitate an expiation for me, and what if I were to say: "The sun god among the Pharaohs"?

As long as you erred and did not intend what you said, there is nothing upon you, for the sin of error is lifted from the servants; due to the Almighty's saying: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts have intended." And due to the Prophet's (peace be upon him) saying: "Verily, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are forced to do." And your statement "the god of the sun among the Pharaohs," if it was merely an informative statement, then there is nothing in it. As for your friend who swore by his father's mercy, he should refer to Fatwa no. 95542.