I strongly disagree Frances. Just because you (maybe me also) would double with AQ987 and out doesn't mean that everyone would. If just 25% of people would not double with that hand, then that is a very significant inference.
Raise to 2♥. I've never played 12-14 in an overall standard context, but I'll assume that I'm supposed to do the same thing as if I were playing 15-17 and had xxx AJx Axx Axxx. Since I can't have balanced minimums like that, I assume the raise shows a better hand than it would if I were playing 15-17 notrumps. Thus I'm either showing an unbalanced minimum or a balanced 15-16 hand that falls short of a raise to 3♥.
South is more likely to have any outstanding high cards because of the double (with AQ987 and out he may not have doubled). North is more likely to have any outstanding diamonds because he has shorter spades. This makes (1) playing South for the ♦A a clear favorite, besides the reasons gnasher stated.
4♠, 5♠, N/A If partner has the 4-4 majors hand (which you said is a good hand), he would have doubled 4NT. Therefore he has 5-5 and a weakish hand. If he could have less than 5-5 and a weakish hand then the methods are stupid IMO.
Because partner otherwise can't tell the difference between when we were bidding it based on a hand that expects to make opposite a dummy with one or so helpful high card (like this one) or a hand that is a classic preempt, e.g. x KQJTxxx Kxxx x.
I wonder if this would happen in real life though. An interesting experiment would be to repost this hand in a year and have several prominent posters put strong arguments out for passing 1NT early in the thread.
I am sure 4♠ over 4♥ should be to play. 5m is worth having an agreement about. I would bid 5♠ here and then pass whatever red suit partner bids, or bid 6♦ over 6♣.
1. Pass 2. invite in clubs 3. Stayman then pass 2M or bid a non-invitational 2♥ over 2♦ (close to just passing 1NT) On (3) I would blast game at IMPs if partner bids 2-Major, but we don't need to even invite here since we will beat the people declaring 1NT if game makes.