My answers:
1. 4NT in this auction does not require an alert, whatever it means. See the ACBL
Alert Procedure, particularly item 3 under Part II, and Part IX.
2. Yes.
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Law 20F2: After the final pass and throughout the play period, either defender at his own turn to play may request an explanation of the opposing auction. At his turn to play from his hand or from dummy declarer may request an explanation of a defender’s call or card-play understandings. Explanations should be given on a like basis to F1 above and by the partner of the player whose action is explained.
Law 20F1 deals with questions during the auction. The relevant part, imo, is
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He is entitled to know about calls actually made, about relevant alternative calls available that were not made, and about relevant inferences from the choice of action where these are matters of partnership understanding. Except on the instruction of the director, replies should be given by the partner of the player who made the call in question. The partner of a player who asks a question may not ask a supplementary question until his turn to call or play.
Also
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Law 20F3: under F1 and F2 above, a player may ask concerning a single call, but Law 16B1 may apply.
and
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Law 16B1: (a) After a player makes available to his partner extraneous information that may suggest a call or play, as for example by a remark, a question, a reply to a question, an unexpected* alert or failure to alert, or by unmistakable hesitation, unwonted speed, special emphasis, tone, gesture, movement or mannerism, the partner may not choose from among logical alternatives one that could demonstrably have been suggested over another by the extraneous information.
(b) A logical alternative action is one that, among the class of players in question and using the methods of the partnership, would be given serious consideration by a significant proportion of such players, of whom it is judged some might select it.
* i.e., unexpected in relation to the basis of his action.
3. Yes.
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Law 20F5: (a) A player whose partner has given a mistaken explanation may not correct the error during the auction, nor may he indicate in any manner that a mistake has been made. “Mistaken explanation” here includes failure to alert or announce as regulations require or an alert (or an announcement) that regulations do not require.
(b) The player must call the director and inform his opponents that, in his opinion, his partner’s explanation was erroneous (see Law 75) but only at his first legal opportunity, which is (i) for a defender, at the end of the play. (ii) for declarer or dummy, after the final pass of the auction.
The emphasis is mine (most people either don't know they're supposed to call the TD, or know, but don't bother)

. Law 75 gives examples of when Law 20F5 applies, and is too long to post here. You can
look up the laws on the ACBL website. Note: since the question was asked during the play period, if dummy mis-explains, declarer should imo call the TD immediately and correct the explanation. Dummy is in a more difficult position, if he disagrees with declarer's explanation, since he is not allowed to call attention to an irregularity (Law 43A1(b)). He must wait until the end of the play (at which time he is no longer dummy).
tl;dr: I agree with the previous posters. The director's ruling was correct.