Here's what you're trading for the alertness feat if you don't take the abil score upgrade and instead take the feat:
- +1 to damage
- +1 to hit
- +1 to AC
- +1 to Dex saves
- +1 to Dex checks
- +1 to init
The question then, ultimately, becomes, is +5 init (net +4), no surprise and no advantage on attacks against from hidden opponents worth it.
The latter two features are very dependent on your campaign and DM. Surprise should be a fairly frequent occurrence on both sides of combat, but that still depends on how willing your DM is to allow it or stage his monsters to have them obtain it (and kind of how cautious your group tends to be). Monsters attacking from hidden is another one that really depends on your DM, you group and how well you guys are at nosing out monsters from the shadows.
So ignoring those two items since they are DM and campaign dependent (and thus can't be weighted objectively), the question then becomes, is +1 to Dex more or less beneficial over 4 levels than +5 to init.
For pretty much any character other than the Assassin Rogue, I'd probably argue that they should take the stat upgrade early, the feat at L8 and then the last stat upgrade. However +5 init has amazing synergy with the Assassin Rogue and you're going to get a ton of mileage out of it.
If you're already at 20 Dex (if you managed to start at 20, or 18 and are at L8), then there really isn't any stat upgrade that is worth taking over this feat (though there may be better feats). Rogues are skill monkeys, yes, but +5% in a single ability set of skills is not worth the +25% to initiative and other features o this feat. The only one that would be worth considering at all is Con for the extra HP, but it's really not that many and you're better of boosting your damage significantly.
Take the feat at L4 (or even better, play a human and take it at L1).
You could certainly Dash first to increase you movement allowance, then attack the first mook, then move, then attack the second mook. That's not exactly what you're asking about though, since you want to see the result of the first attack before deciding to Dash.
In the strict rules as written, however, only movement is explicitly allowed to be broken up arbitrarily. Taking the Attack action doesn't "add to your attack allowance" the way Dash adds to your movement allowance.
Implicitly, when you take an action, you are committed to completing the entire action unless you have a rule that says otherwise. "Moving Between Attacks" is one such rule, and object interaction (PH p.190) is another:
You can also interact with one object or feature of the environment for free, during either your move or your action.
By this reading, you have to complete all the Extra Attacks that are part of the initial Attack action before using Action Surge to Dash.
Best Answer
Yes, this is legal
As long as you hit with both attacks -- the one on your turn and the one on your ally's -- you can autocrit with Sneak Attack damage on both. All the requirements of Sneak Attack and Assassinate are fulfilled.
Other builds that can do this
These MC builds achieve the same thing at a later level, but here's to illustrate that you can do this without Action Surge, using just your regular Action.
A Sorcerer 3/Rogue Assassin 3 with Quickened Spell
A Wizard 5/Rogue 3, or Sorc 5/Rogue 3, or Lore Bard 6/Rogue 3
A Frenzy Barb 3/Rogue 3, Strength-based