"In the queue" is now "ON HOLD." The way it's been working lately is you'll click on the link that is posted on runDisney.com, which will take you to an Active.com page. All of the events will be listed there, and you'll click the radio button for the one you're registering for. If the queue for registration is currently full, the button won't be there - it'll say "ON HOLD" instead. There are instructions on that page to refresh until the button comes back, if it comes back.
I saw that happen during Star Wars registration - the 5K and 10K alternated between "ON HOLD" and the button being there. I'm not sure how you know when you're out of the queue.
One thing to keep in mind with the DVC/AP registration is that it's a small number of slots that they're allocating for tomorrow - I've heard it's something like 5-10% of the total registration spots. That way there are some left over for the rest of us.
Yes, you can start in the same group. Everyone gets assigned "starting corrals" at the expo (lettered A-P...there's also an elite corral). A starts first, then B, etc. The runner assigned in the higher corral can drop back to the latter corral, but not the other way around (example: if you're in C and your son is in E, you can drop back to E to run with him, but he cannot come up with you to start in corral C). Your corral will be printed on your race bib.
It won't sell out in 5 minutes (and if I'm wrong all of you can come back here and shame me). It'll sell out quickly (again, see above with the whole "limited number of spots" thing), but not in 5 minutes.
HOWEVER - if you want to sign up for the 10K, yes, that'll sell out quickly. The 10K is a popular distance, and a good number of spots are reserved for Glass Slipper Challenge participants.
On registration day, you'll need to log into your Active.com account to sign yourself up. You can also sign up your son (since he's under 18) from your account. The good news for you is that since you're DVC, you get 2 chances to register - tomorrow and then July 14, if you need to. Alternatively, if you decide to sign up for the half instead of the 10K, it should be less pressure - lately with rD races the challenges and 10Ks have been selling out the fastest (30-45 minutes), then the 5Ks, and then the half marathons.
In your case I'd decide between yourself and your son which race you REALLY want to do, and go for that one. Be ready to go tomorrow at noon!

EDIT: Missed your last question about the 10K - is it as fun as the half. I haven't run the Princess 10K yet but I did run the WDW 10K in January (which is the same course). You don't run through Magic Kingdom (so no run down Main Street/through the castle) but you do run through Epcot and the Epcot Resort Area. I actually like that course better than the half course (personal preference). So yeah, it's just as fun in my opinion.