They are not interchangeable, but can have the same meaning. When でも is used to mean “but”, it must (contrary to good western style writing) be at the beginning of the sentence. そして “and then” works the same way.
I would say that が and けど・だけど are basically interchangeable. でも can’t combine sentences, it can only start a new sentence (more like however works rather than but in english). I’d also say that its better when you’re introducing a contrasting point that is also a new idea to the first.