Should I log flight time as a passenger?
No, you should not*. 

In my opinion, you should limit your logbook to records of your own flight experience. This would include any time spent training, as PIC, or as required crew.

The time you can log as PIC is that which you spend as the sole manipulator of the controls, the sole occupant, or as the pilot in command when the required crew is >1. Here's an article from an FAA FSDO describing the logging of PIC time in more detail. Rod Machado has some good coverage of this as well.

If you're just hanging out in the airplane, it doesn't matter if you're in the front seat or the back seat. If you're receiving instruction, you should get an entry and a logbook endorsement from the instructor you're flying with. Most General Aviation aircraft don't require a type rating, so I'm unsure what the context of your final question is.

&nbsp;

* It's worth noting that you can technically put whatever you want in your logbook, though it's not a great idea; when it comes time to fill out an FAA 8710 form for later ratings, it can get confusing. In my opinion, you still shouldn't log any time, but if you're just wanting to record flights that you took with friends, that's fine. As an instructor who's had to slog through some weird logbooks, I'd really, really encourage you to track that elsewhere, though. Your logbook is exactly that - it's your logbook, for the logging of your flight time, and a record of your flight experience and training.