This has nothing to do with imperatives - it's just about standard verb combinations.
The verbs 'go', 'come' and 'run' can combine with other verbs to suggest a single action. In AmE this is "verb+verb" ( as in "Come see") while in BrE this is "verb+and+verb" ("Come and see").
This is my view, from a British English perspective:
1. This is grammatically OK, but a little odd. We usually say "go to + verb" to emphasise the reason for going to a particular place (infinitive of purpose).
2. This is normal in AmE. It sounds typically American to the rest of us. I would say "Go and get the bag".
3. Same as 1. Possible but not natural.
4. Same as 2. I'd say "Run and get.."
5 and 6 "Hurry" doesn't work like this.
"Hurry" and "catch" are two separate actions , so you can't combine them in this way.
With "to", this would be an infinite of purpose - you do one thing in order to achieve another. For example, ""I hurry to catch the bus every morning". This doesn't work as an imperative, though. You'd have to say, "Hurry! Catch the bus!"