I'm going to DLP in a few days - the two parks close at the same time as each other every night, and so I believe on weekdays the Star Wars show will be at 7.45 and Dreams at 8... and at weekends there'll be two Star Wars shows but the later one will again start just 15 minutes before Dreams. Do they really run back to back? And if so, I assume it's not really possible to watch both on the same day (other than a weekend when there's an earlier Star Wars one)?
That is correct.
At the weekend the English version of the Star Wars show happens first so perfectly possible to see that then dreams. During the week you'll have to pick one or the other.