Maybe not, but she does call him “Director”, which seems like a pretty specific leap from “lead government chump in a suit”.
Maybe. We shall see.
Of course, she also singled him out from quite a distance in the dark to toss the drone at his feet and ask if it belongs to him (and, yes, she is singling him out; Monica and Woo are right there and she ignores them).
I think in that scene, he's at the center of the formation, giving orders, but not in tactical gear or holding a gun himself. He kinda stands out.
It certainly seems like she expects to find Hayward there.
Again, perhaps. But, let us consider - the question is why she leaves him alive....
The answer is simple - she's not actually a villain and killer. She thought she was, back when she thought she needed to make Stark pay, but, interestingly, she didn't kill him.
She has what she wants, or as close to it as she's likely to get. Killing him (or any of the Agents) does not get her anything. It would serve no purpose. So, she doesn't. In fact, she shows remarkable restraint, all things considered - which is a sign that she's not really a villain.
5 years later? Maybe. But that’s a very cold trail, especially given that she’d be starting in Wakanda.
No, she's not starting in Wakanda. There is no reason at all for her to go back to Wakanda. Why would she go there?
She gets snapped back, and takes part in the final Endgame battle. After that battle, her next question is "WHERE IS VISION?" The place would be swarming with SWORD agents trying to debrief (as I already noted). They would be seeking her out. She can start by asking nicely, and would be given the runaround. A few days or weeks of that, she'd eventually get fed up, but by that time she's talking to someone who actually knows what's up, and she can make their mind an open book...