no they don't
no they don't
Depends how you define Catholicism. Some RCs deny EOS are to be called Catholic, thus they take offense at "Roman Catholic" in making that distinction.
You claimed: "rejecting Catholicism is rejecting the church that Christ founded and thus rejecting Christ". The Eastern Orthodox DO reject that the Roman Catholic church is THE, one, true church Christ established. The EO reject the dogmas that the Pope is infallible, that he is the head of all Christendom, they reject Purgatory and the immaculate conception of Mary. Curiously, these are also areas many not-Catholic Christians also disagree with Catholicism.
So, unless you are playing a semantics game with the word "Catholic" - you wouldn't be the first here to do that - genuine Christians can and do reject Catholicism as the church Jesus established and they are NOT rejecting Jesus by doing so, just believing God.