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).
No, critical hits must be linked with attack rolls.
I checked with Jeremy Crawford on Twitter and he says that critical hits must come from attack rolls:
@JeremeyECrawford No, since only attack rolls can score critical hits.
In response to @Kevinaskevin Can my Rogue's Assassinate cause my Wand of Magic Missile to crit against surprised creatures?
You should read the full conversation between he and I to get more detail.
Critical hits come up in the PHB on pgs. 194 & 196. As I see it the PHB pg. 194 text doesn't imply that critical hits are exclusive to attack rolls:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target’s AC. In addition, the attack is a critical hit, as explained later in this chapter.
PHB 196 describes critical hits but never uses the words "attack roll". Reading the text above someone new to DND could reasonably assume there are other causes of critical hits.
Despite this, Jeremy made it clear that the game designers intended critical hits and attack rolls to be linked.
Best Answer
For reference, here is the Assassinate ability:
So, the Assassin does, in fact, get advantage, since Alert only prevents advantage from being hidden, not advantage from not having acted yet.
But, since you can't be surprised, the Assassin doesn't automatically get critical hits on you. Even if they did, they'd still need to land a hit.