She actually did well considering she isn't a stalker by now. That means she must be resourceful, agile, quick, and good with her hands to evade the metropolice. Since a gunshot would basically make more come just like they caught Gordon Freeman, and if she gets shocked by a baton its Nova prospekt for her.
A lot of things that isn't told to you directly, and slow change and not much talking would be expected when you are basically a lone wolf in a dystopian world. Elizabeth felt too fast changing, and unbelievable. When she was dancing with the people on the beach and being talkative and friendly to everyone it finally struck me that its most likely not how a highly socially isolated person would react.
Liz hated me, but still was friendly, then became my "friend" again 30 minutes later. It felt like the developers put so much effort into being friends that they forgot to tone it down and put in context. For example, Its like being followed by Pinkie Pie. The character tries too hard to show you all off her tricks, just like me trying too hard to be someone's friend would creep people out.
The message I kept getting is "do you like me yet? huh, huh, huh?!" with some overly dramatic theatrics. It was like watching a cartoon, or a movie on the sci-fi channel rather than an actual person.
Alyx doesn't have that issue. Because normal people don't act like that, at the ones I know don't, not everything is accompanied by exaggeration of body motion. She just talks relatively like a person would. Not everyone shares every single portion of their life like an open book, either. Sometimes, the trick for a good character is not to talk about everything under the sun, but show it through action. Not everyone is an extrovert, some people keep it to themselves. The commentary from valve on Alyx is that they cut some lines they thought were too "gamey" like her magically knowing what the reactor of the citadel looks like, even though the resistance had issue with spy networks on the higher end of the chain of command.
As for heroics, actually Dr. Green was slacking. His speech in Nova Prospekt was that he could arrest Eli in the past 10-20 years, but he tries to use excuses as to why he wasn't doing anything. It seems the G-man, the one running the show and has reality bending powers, was helping the resistance. So Gordon was a tool, not even the main guy doing most of the work because the G-man seems to be there before Gordon even arrives. Unlike the vox populi, who didn't have anything going for it because they couldn't even scavenge guns and had only knives.
Then again, they didn't explain what the G-man is, or why he does anything.
