If you drop to the IRR like I did (first job out of the Navy had me working in Dubai, Russia and Africa), it is a MAJOR pain in the rear to get back on SELRES. Think of just as much work as getting into the Navy in the first place, minus NOMI and OCS/ROTC/CanoeU.

1) I heard you should never tell people you're getting out until you drop your letter. When do I have to drop the letter?
If you 2XFOS, you don't have to drop any letter, they drop it on you.

2) When should I sign up for TAPS and does that let the cat out of the bag to BUPERS? How would they know? Don't bother until you have separation orders in hand. TAP is kind of useless for JOs getting out. It's geared towards one term junior Es and guys retiring.

3) Would dropping my letter or attending TAPS (or anything else you can think of) make me ineligible for the severance pay?
Don't get ADSEP'd for PRT, DUI, etc. Other than that, you get it.

4) How exactly does one obtain the severance pay? Would I have to sit on my butt going months past my MSR watching my buddies get better hiring seniority in the airlines?
You get 2XFOS. You sign paperwork accepting a IRR or SELRES commission. That's it. The money shows up from DFAS in your last AD paycheck.

5) When should I interview with the airlines?
As soon as possible. Give your projected availability about a month before you run out of terminal leave. (my terminal leave was partially cancelled, so I ended up cashing out 30 days of the 90 I had)

6) Considering I will have 2 months terminal leave, should I plan on classing up with the airlines then?
You can hope to. I got out in February 2012, I've still not even had an interview with a major, and can't work for a regional due to the inability to live on $15k a year (ex wifes gotta eat and make her condo payment ya know).

7) If I'm committed to getting out, should I take the DH bonus?
If you are confident you WILL FOS. Then why not. I got 3 of 6 payments. But, I also took it planning on staying in for 20, before the selection rates went to hell.