1) Why would he not have a huge backing? He's an avenger, he was left with responsibility of Stark tech. Why would Pepper/Happy/Shield not be able to help him? Plus, this is the much more obvious route to try first before asking for a spell to be casted across the world.
I don't disagree with the question. Between Civil War and Infinity War, all Peter had was the suit Tony gave him. Tony did offer the Iron Spider suit and full Avenger status, but he initially turned down both. From that point to Infinity War, it was more or less implied that Peter was on his own, being a friendly neighborhood Spider-Man. He probably could've asked Tony for help plenty of times, but he seemed fine handling things on his own, and nothing came up that really warranted that help. And Happy did help him and May, he let them stay in his condo while everything was happening. If he could've done more than that, don't you think he would have? As for S.H.I.E.L.D (which still doesn't exists anymore), Peter clearly had no way of getting in touch with Nick Fury, and he didn't even know he was in space. Pepper, maybe he could, and she did donate to the charity May was working for. She knew Peter, and knew he was important to Tony, but she didn't seem to have that much of a relationship. Any aid from her most likely would've come through Happy, and like I said, if he could've done more, he would have.
2) It's 100% more than a handful of people - there was that scene where he grabbed the gauntlet and handed it to the female teams - so all those females know who he is. And from there, it's not hard to imagine how quickly that spreads (e.g. WASP would tell Antman, her dad etc.)
Wasp is gonna tell Ant-Man what, exactly? That Spider-Man is some random kid in red tights? The only person there who even knew his face and name was Pepper, and she's definitely not gonna go telling everyone. As for the rest, like I said, they have more important things to be concerned about than whoever this kid is. Most are aliens who definitely don't care (the Guardians and Asgardians), Wakandans who couldn't give less of a shit (Okoye especially), Captain Marvel (who cares as much as the aliens), and Wasp (who I would bet two paychecks that she cares as much as the rest). They don't care, and why would they? Spider-Man isn't really that well known outside of New York yet, and they have zero incentive to go and figure out who he is.