This is my take on it (I'm no expert and don't know the finer details of your relationship). I'm basing my answers on RWS deck.
#1. Where is his mind/ heart right now? The hierophant and 3 of wands
Tricky one as you've asked about two different aspects and drew two cards. The way I see these cards are:-
Mind - Hierophant. Dictates he should 'do the right thing' and accept your apology.
Heart - 3 of Wands. This outburst is new territory for him and suggests he's examining how to move forward through it.
#2. What should I do (say something or not): 9 of pentacles
This is, for me, the strong, independent woman card. However strong the urge is to open dialogue about the incident, you're best off not, unless it is him that brings about the discussion. More details about that in card 4.
#3 What does he need from me? King of Cups
I agree with your interpretation, a bit more emotional control and understanding (he probably already felt bad about bailing on your date).
#4: future / will we overcome this? 6 of cups
Maybe he'll turn up with a bouquet as way of apologising to you
Seriously I don't feel this is going to be a game changer, he'll turn up and you guys will get back on track.
The interesting thing I picked up on this card (where it ties in with 9 of Coins), maybe you need to address something from your past. Where do these feelings of being let down come from? Did a previous partner or absent parent let you down leaving you feeling as though you'd been 'abandoned'? Did someone always appear too busy with work to spend time with you and the only attention the offered was when you became angry/upset?
If this is so, then it is up to you to address them and not project these issues onto your current partner (y'see the strong, independent figure on her own dealing with her stuff?)
Bottom line is, don't try and talk it through unless he wants to, most men don't like the 'let's talk about our feelings' thing, it scares them lol.
Hope that sheds some light on it. And I hope he knocks on your door with a huge bunch of flowers, a bottle of wine and tells you he's sorry he upset you