Yes, many formats are read start-to-end, but I don't think that's a requirement. The important thing is it can be stored and transmitted as a stream of bytes. The word describes how it is transported and stored, not how it is read.
Yes. That's precisely what "random access" means.
> The important thing is it can be stored and transmitted as a stream of bytes.
What isn't stored and transmitted as a stream of bytes? Memory itself is a sequential array of bytes. The criteria you're using here seem to be all-encompassing.
When we're talking about serial access to data, it means that we're sequentially parsing the stream of bytes from its starting point, rather than reading arbitrarily from any point in the stream that we desire.
Yes, by your definition, this is random and not serially read.