I guess I can't relate to Garfield's brand of awkwardness, because when I was a teenager, I was definitely more like the Maguire version of Peter Parker; really shy, soft-spoken, bullied, low confidence, etc. Garfield's awkwardness comes across as "attention-starved" to me (not accusing you of being that way, by the way- Hope I'm not coming across as if I am saying that!), whereas I've always felt that Peter Parker himself was too meek to want attention like that. That's why I've always loved how he becomes the confident, witty, and sassy Spidey when he puts the mask on. One of the lines I actually loved from the first TASM was "Put the mask on, it will make you stronger." That's how I've always felt about Peter's feelings towards the costume and the persona. That's why I think these new movies have missed the mark on Peter Parker, personally. I think the TASM movies have come into their own when dealing with Spider-Man's persona, though. I think these movies "get" Spidey's personality. I don't think that's the case with Peter Parker, though (in my personal opinon).
Also, I just find Garfield unpleasant to watch in these movies as Peter; not because of some "social awkwardness," but because I think he sucks the life out of many scenes for me. Most of the other actors/characters don't do that; but Garfield's Peter does (for me, at least). It makes the movies really unpleasant for me to watch. I don't think that's social awkwardness; I think it's a style of acting that's simply not in tune with the other actors (and I think Peter's scene with Aunt May in TASM2 demonstrates that, as the scene was totally working for me until Peter spoke; maybe that's just the screenplay/script ruining those scenes for me? I don't know).
As for the car accident scene, it was incredibly stupid and thoughtless for Peter to walk in the middle of the street like that. The scene came across as a really hokey attempt to show that Peter is so "in love" with Gwen, that the sight of her makes him all goo-goo. I don't think it was because Peter was confident in walking because of his spider senses. If that's the case, then he really is a *****e, because other people don't have spider senses. Also, being the cause of a minor accident instead of a big, serious accident is okay? Ehhh, no. Peter's kind of a jerk if he's okay with causing minor and inconvenient accidents to people who can't anticipate when he's going to walk into traffic.
And Peter doesn't care about Uncle Ben in these movies. Aunt May seemed to be the only one to ever mention him, and Peter was only focused on his parents and Captain Stacy. I never got the vibe that Peter really cared about Uncle Ben being gone in this movie. If the movie was trying to convey it, I think it failed miserably.
The traits you listed though are universal when it comes to social outcasts/awkwards. Things like shy, bullied, low confidence, etc. are shared by both the Tobey Maguire and Andrew Garfield types, which we even saw those traits in this Peter in the first film. At this point though (post-high school), he's grown a bit past that, which was true about comic book Peter too. He often talked back to Flash, even challenging him to a boxing match in front of the whole school back in one of the early Lee/Ditko early issues.
To a certain extent though (just in general), Peter always did have a bit of that snarkiness to him even when out of costume, though that aspect at that point in his life was only explored in-depth later on. Basically, it was a coping mechanism to hide fear/anger/sadness with humor. I used to do the same when I was a kid. It wasn't as "out there" as Spider-Man's wisecracks though, more like shrugging things off. It's not so much that Peter is a mute while being Peter then a wisecracker as Spider-Man. It's more like Peter is about as witty as the average socially awkward dude (who has a few lines here or there) and then Spider-Man is that fully unleashed. It's his inner troll being let out

. Plus, we only see him like that with characters like Gwen and Aunt May, and it makes sense he's a bit more comfortable around them, but he still does/says "off" things due to that awkwardness.
I know you're not accusing me of being that, so no worries. Funny thing, I actually got that sometimes as a kid. "You're not funny, stop acting that way." Some even said I sounded weird/awkward. Heck, remember those facial/hand ticks he had in the first film? I used to have those too. Others told me I always looked uncomfortable in my body, which is also true about this Peter (i.e. the scene where he tells Harry about Spider-Man's sensitivity from the spider-sense, which is true about some spiders in real life). To make this clear though, I wasn't a freak or anything. I still dressed good, looked decent, had friends and was well liked at school/job interviews, but I still had that "not in tune" aspect you would notice if you got to know me. Which stems from the bullying/outcast from my early childhood. Much like Peter Parker and particularly this version.
Regarding the street scene, it was a bit of both. Yes, Peter did have the "wow" love feeling for Gwen, and his spider sense - the lack of danger, that is - made him cross the road like that. It wasn't him being all like "Hey look how cool I am for crossing the road like that cuz I have spider sense." I also brought up how Peter's spider sense warns him of danger to him
and innocent bystanders. We see this in both movies. If there was any car damage or anyone got hurt, he would have known about it before it happens due to the spider sense, and would have taken action.
Also, why am I analyzing so much the question of "Why did Peter Parker cross the road?" What am I doing with my life?
As for Uncle Ben, May and Peter talk about him several times. About how they wish Ben could have been there at Peter's graduation, how Peter is trying to help May with the bills ever since Ben's been gone via the DB, May's whole speech at the end about moving on, had a picture of Ben's killer on the wall he made where the "Am I gonna lose you too" note was attached, etc. Could the film have benefitted from more Ben? Absolutely - there is
always room for more Uncle Ben in Spider-Man stories. But given everything that was happening in the film, I didn't mind it not being as much in the front. I already know the origin and got to know Peter as a character in the previous film. I didn't mind it for the same reason I didn't mind the Waynes never being brought up in TDK. A lot of people criticized TDK for that as well. That's understandable, but it isn't a big deal for me.