No.
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Null hypothesis of a one-way ANOVA is that the means are equal. Alternate hypothesis a one-way ANOVA is that at least one of the means are different.
Yes, usually.
YES!
The process is called hypothesis testing. If you are inquiring on how to prove or disprove a claim, search for the article on wikipedia.
Neither. It is a hypothesis which may be true until proved or proved to be false.