Traffa is a bit relaxed and maybe random whereas mota is formal and usually planned...i think
I'd be generally inclined to agree, but it's not quite that simple. There's a very, very large amount of overlap. For instance, jag mötte henne på stan i går sounds very informal.
Yes. A crown princess is the heir to the throne, whereas a "non-crown" princess has to wait in line (i.e., the former is the firstborn, and the latter is not). At least this is the case in Sweden.
The Swedish crown princess's younger brother was actually crown prince for about year, before the law was changed in 1980 to make the first-born child, independently of gender, the heir.
I accidentally submitted a report on this question because I'm an idiot and wasn't paying attention. I can't find a way to retract it. Sorry!