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).

Grappling is not two-way

When someone grapples you, they are not automatically also grappled by you.

Using at least one free hand, you try to seize the target by making a grapple check [..] If you succeed, you subject the target to the grappled condition (PHB 195)

Note that only the target gains the condition.

Thus both bullet points of the feat refer to the same situation: when you have successfully grappled a creature and they have not escaped yet.