"Mötas" and "träffas" can both be used to describe that two people meet:
Vi möttes på torget / Vi träffades på torget
"Tågen möttes" is a correct sentence to describe that the two trains were running in opposite directions, on different tracks :), and passed each other. Here, träffades does not work since we are not talking about living beings.
"Jag träffades av tåget" actually means that you were hit by the train. You can also
träffas av blixten (lightning)
träffas av en kula (bullet)
Does this mean they come across each other at the museum or they arrange to meet there?
Can I translate på as "on" here? For the unlikely situation of meeting someone on the roof?
I've seen some examples in Swedish that use "i" instead of " på". Would it be correct to say 'i museet" in this sentence or would it only be correct if you specifically meant we were meeting inside of the location?
i museet is not technically wrong, but it sounds weird in the way that saying "we meet on the inside of the museum" sounds weird when you mean "we meet at the museum".
So how does one specifically tell someone to meet inside the museum as opposed to outside?
- Vi träffas inuti museet = inside
- Vi träffas utanför museet = outside
These both work well idiomatically.
This is the first present tense verb I have noticed that does not end in r. Can I expect to see more?
Yes, there is a full set of verbs ending in -s despite not being passive. These are called "deponent verbs". However, träffas is actually just the passive form and those pretty much always end in -s, so it's not a regular present tense.
Then there are also a couple of irregular ones, some of which you've probably seen - like jag vet, du kan, etc.