Not exact about RAW, I'll try to dig up some info tonight after work.
Here's how I do it. If I'm wrong, one of these friendly and knowledgeable people will correct us.
1) No. I have played like you describe, but found it too powerful. RAW is that movement lowers Init by -1/10% moved (RMSS pg 74). So if you wait until the guy runs up to get closer, his init will suffer, but it's not guaranteed that you have init. IMHO, Opportunity Actions change the phase you act, not the init.
2) Changing Action is -40 OB. I believe the Opportunity Action must be declared.Then it can occur on the next phase.
RMSS:
"Example: Dral has already moved 20' (20% activity)
during the Snap Action Phase. Dral has a declared
melee attack normal action (80% activity)
against Morg the Orc. However, Darien knocks
Morg unconscious with a spell early in the Normal
Action Phase. Having no active foe, Dral decides to
cancel his declared action. His canceled actions are
more than 60%, so he can move over to another foe
using half his normal movement (50' at a run)."
-But can't make an attack. The example is not an Opportunity Action but I included it to be more descriptive.
Keep in mind RMSS pg 75;
"Note: If part of a character’s OB has already been
used to parry a foe (see Section 23.2.6), he may not
cancel the related attack action."
If you're already in Melee, then you probably have declared an OB/DB split. If you parry (use DB from OB) you can't cancel the action.
3) I'm pretty sure that penalties from acting in a "phase" only apply to that phase. Since you didn't actually make the missile attack in snap, you don't get the -20 for firing in snap.
Now depending on the phase you act, it will limit the %Act for movement and can modify OB as normal for
that phase.