They're not always interchangeable. Kreth has a point that möta tends to be more formal in some contexts, but also, if you want someone to meet you when your train arrives, you can say Möt mig vid tåget but träffa doesn't work.
möta can have a more neutral meaning. For instance if you're describing two people who are walking towards one another, at one point they will mötas i.e. be in the same place. But for them to träffas, they would have to do something more than just pass one another. For the same reason, we say that parallel lines do not meet using the verb mötas, but träffas would sound funny.
Also, träffas can be the passive of the verb träffa meaning 'hit' so that att träffas or att bli träffad can also mean 'to be hit' like for instance in being hit by lightning.
It's not old-fashioned per se, people use the word all the time. But the meaning changes. When folk is used as a countable noun, it means 'peoples' as in 'populations' or 'nations'. So the reason it doesn't work here is much the same as why you wouldn't say you want to meet 'new peoples' in English.
There is a rule, but människa is an exception.
The rule is that before so-called "soft vowels" (e, ä, i, ö, y) , sk is not silent, but the infamous sj-sound. It varies by dialect. As a native English speaker, I generally pronounce it as something like "hw", but sometimes it's more like "sh".
Before "hard vowels" (å, a, o, u), sk has a hard k sound, like the English word "skate".
It feels natural, after a while.
Then there are exceptions that follow neither rule: handske has a hard k sound, människa has the sj-sound, etc.