Peter lost his powers owing to psychological distress, self-doubt, and his lack of motivation because of his financial issues, relationship problems, and educational struggles he was going through. Peter doubted his choice to be Spiderman and hated himself because he could not balance his normal and superhero life.
The Amazing Spider-Man cannot shoot organic webs because the spider bite gave him all the powers of a spider but did not grant him the ability to spin natural webs. In the comics, when Peter is bit by the radioactive spider, he gets all his powers – super-strength, agility, the ability to climb or crawl on any surface, and most famously his spider-sense. But, still, he is unable to produce and shoot organic webs, so he creates his web fluid and mechanical web-shooter to be more like a spider and justify his name.