Do all published manga originate from one-shots? I heard that some popular manga (for example - Naruto, Nurarihyon no Mago, Beelzebub) are published as one-shots during their first try. I want to know if that applies to all manga or not? Would many manga be published as a one-shot first?
It doesn't apply to all manga. For instance there's manga that are adaptations of other works (anime, video games, light novels) which don't start off as one-shots and have, at the very least, a contractual run. Additionally, there are also manga that are used originally as promotional, as advertisement for a store or an upcoming anime.

The Evangelion manga is an odd-ball, where it was supposed to be an adaptation of the Neon Genesis Evangelion anime series, and start a month or two before its TV run as a promotion for the anime, but the TV run was delayed and didn't actually air until a year's worth of manga chapters. Additionally, there's several recent spin-off manga loosely based on the series.

There's a bunch of Gundam manga that were adapted from anime that were never one-shots. Slayers has several manga series that were adapted from the anime and light novels. Cowboy Bebop, Blade of the Immortal, etc.