Adding "re" prefix
Solution 1:
Henry is of course technically correct: You can't just slap re- onto any verb. But I believe the spirit of your question is: Are there verbs that are correct to put re- in front of, even though the result is not in the dictionary? And further, are these plentiful enough that your friend was merely being sloppy in their phrasing, rather than wrong in spirit?
My answer: Definitely yes, and yes.
My dead-tree American Heritage Dictionary even has this note following its entry for re- (note the first sentence):
Usage: Many compounds other than those entered here may be formed with re-. In forming compounds re- is normally joined with the following element without space or hyphen: reopen. If the second element begins with e, it is preferable to separate it with a hyphen: re-entry. However, such compounds may often be found written solid and are indicated here as fully acceptable variants. If a compound that resembles a familiar word is intended in a special sense, the hyphen is necessary to make the distinction: re-creation, meaning "creation anew." The hyphen may also be necessary to clarify an unusual nonce formation: re-realignment, or a compound that produces a series of three or more vowels: re-aerify.
Solution 2:
It should be extremely awkward (or just plain wrong) with stative verbs. Re- has an inherent notion of repetition (obviously), and stative verbs "have no duration and no distinguished endpoint".
So rewant, rebelieve, re-be, and so on, just don't make much sense, unless you have a really special context (or, if you use a non-stative form of the verb, but not all stative verbs have non-stative counterparts).
Solution 3:
No. For example your suggestion would not work with I am, I may, and many other simple verbs.