0 - Not deux ex machina. Hank had just spoken with Jesse at the police station. It's highly probable that Hank was tailing him after he was released.
1 - He didn't remember the numbers at first, but it's highly probable that a person with a mind for Chemistry could eventually over the course of a few hours, let alone days, memorize a set of 6 numbers.
2 - Not sure what you're referring to here.
3 - So the bad guys didn't have "follows directions well" checked next to their report cards; not exactly sure what's so silly about this. In addition, Jack later reveals his suspicion that the numbers were more than what they appeared.
4 - Already addressed.
5 - Seems like your average scene to me.
6 - I have addressed this, in depth, in the past, but I'll give you a summary. Huell sleeps on the job. Does he seem like the most reliable person to you?