[Legolas]

As far as I know, you attack at 0, 2 and 4 seconds into the round plus a little delay based on the initiative order (not related to the actual value of the roll, only to how many of your opponents you've beaten in the area you're in. Or somesuch. I'm not convinced this is true). Although if you and your opponent are a distance apart it gets a bit dodgy as sometimes you get an AOO, sometimes the other one does, or they get to strike first once anyway all depending on when you two get within melee range - the rounds 'start' when you're still apart and you first click the enemy.

Spell casting starts at the first moment and takes a certain while to complete, usually a second and a half, after which you're more or less immobile for another second and a half (see spells.2da). So your spell goes off after the first but before the second attack - usually. Not counting an AOO which takes place when you begin your casting.
Haste and Quicken Spell can speed up the casting time, perhaps allowing you to cast a second spell after the first one before the round's ended.

Although since attack and damage are separate, and there's a delay between the casting of a spell and its own effect, it's entirely possible that between getting a hit/spell in and killing your opponent they can still get their hit in before, and deliver damage after they've died.

I find that unless you're involved in a pvp situation where getting your spell or blow off first makes all the difference, initiative isn't really worth thinking about.