Learn English – What word means “things that can’t coexist togther”

There aren't specific rules, but there are general principles — each preposition has a particular "feel" to it, which guides the use in particular situations. And of course there are plenty of idiomatic expressions which simply abandon those principles entirely.

For the question at hand, I would suggest the following principles:

• "On" is used when you ride on top of the transport, rather than being enclosed by it (on a bicycle, on a motorcycle, on a scooter).
• "On" is also used when the vehicle is large (large enough to stand up and walk around) (on a bus, on a train, on a ship).
• "In" is used when you are enclosed in a small vehicle (in a car).

Note that this means that for some forms of transport it's possible to use both "in" or "on", depending on the size: I personally would say on a Boeing 747, but in a Cessna, and I might similarly use both "in a boat" and "on a boat" depending on how large/enclosed I felt.

Also note that the above are not by any means strict "Rules of English" — they are based on how I (as a native speaker) perceive I use the prepositions. I'm sure there are exceptions, and I'm sure people will point them out — but this is probably a good rule of thumb at least for common cases.

What is your problem with condolence? It does not only apply to grief of death, but of any severe suffering. Its origins are similar to sympathy and compassion, all meaning essentially to suffer together (or as the commenter said "I feel your pain.")

However, all three of these words seem to work: I offer my sympathies, or condolences. I'd also say that to say "I'm sorry" only means "I apologize" in some circumstances. "I'm sorry for the terrible thing happening to you" does not in any way imply that you feel responsible, or are accepting any blame.