Here is an explanation.

Yes, but the differences are not integers. To quote your source:
The 27° N latitude passes back and forth across time zones in South Asia. Pakistan: +5, India +5:30, Nepal +5:45, India (Sikkim) +5:30, China +8:00, Bhutan +6:00, India (Arunachal Pradesh) +5:30, Myanmar +6:30. This switching was more odd in 2002, when Pakistan enabled Daylight Saving Time. Thus from west to east, time zones were: +6:00, +5:30, +5:45, +5:30, +8:00, +6:00, +5:30 and +6:30.

The time difference option in the user settings is there in order that you can see when a message was posted at your local time if the forum time is different to your local time.

See this post in the German Forum.

In my profile the time-difference is set to '0', the server sits in Germany (D-74321 Bietigheim-Bissingen), my clock shows 17:34 and the post shows up with the timestamp 16:34. Maybe the server slept over the daylight saving time.

Who deleted my screenshot?

This error will show up only, if I'm not logged in. Otherwise it shows "15:21" for my "Time difference" posting. (Depending on my "Time difference" user setting.)

I don't really understand what you mean. How many days/hours/minutes ago a message was posted is completely independent from the time zone.

In my user settings I have a time difference of "1" (hour). Let's say I post a message at 14:00 local time. I come back after 5 minutes. If I'm logged in, the message will be shown correctly with 14:00 and "Latest postings" shows "5 minutes ago". Then I log out and now the message is shown as 13:00, but "Latest postings" still shows "5 minutes ago". That's confusing! At least to me.

To be honest, I never fully understood the timezone stuff.

Here is an explanation.

I know those pages, but ... To make things even more complicated, they invented the stupid DST stuff.