As far as I can tell what you wrote and what your friends suggested are exactly the same so I can't comment on that, but here are some thoughts on the three numbered sentences:
This is grammatically correct, but is semantically odd as
available isn't generally volitional (although some people use it that way)--it describes a state of being and not an action.
This is not grammatically correct;
available is an adjective and can't be used as a verbal complement to
This is also grammatically correct and is preferred over
will can be used in a non-volitional sense as in "I will be alive tomorrow."
Alternatively, you can also dispense with the modal verb
will and just say, "I am not available from 9 to 10 (am? pm?)" or "I am unavailable from 9 to 10 (am? pm?)"
Also, as a side note,
suggest can't take an indirect object ("suggested me to"). Some acceptable ways to use it would be:
- My friends suggested (that) I do this
- My friends suggested doing this.
- My friends suggested this sentence.
- My friends suggested what I should write.
See this for more information: