All of the sentences you said are grammatically correct, but they are very formal or old-fashioned and they would be used in writing if used at all. In what situation are you using these sentences? If you want to disagree in a more normal situation you can use the word "actually" in the beginning of your sentence. The word "actually" is used to more politely tell someone that you don't agree, and then you won't need to say "I don't agree". For example:
Person A: "I think the Earth is flat."
Person B: "Actually, the Earth is round."
"Actually" can also be used with "I don't agree", so you could say: "Actually, I don't agree with that."
In English, the less firmly you state something, the more polite it is, so any words or phrases you add to the sentence that make it less specific, less direct, or more of an isolated opinion will make it more polite. Using these phrases (or combining them) can make your sentence more polite when you are introducing what you are disagreeing about or stating your opposing opinion:
I think (that) ....
It seems (that) ....
... tend to ....
It's possible (that) ....
(replace regular adjective form with a comparative form)
(replace "is" with "can be" or "could be")
A direct (and less polite) disagreement:
Sports players are rude.
The polite way:
Occasionally, sports players can be a little rude.
Occasionally, sports players tend to be a little rude.
The end of the world is near. -> I think it's possible that the end of the world is nearer.
This movie is terrible. -> Some people think this movie isn't very good.
There are many combinations of these phrases you can use, and this way of disagreeing politely can be used in conversational English or written English.