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Hello Grant and welcome to JA!!!
I'm Billy and i will assist you with this.
These problems, at least some of them are connected (for example the back door and remote operation)........
First you need to check for any blown fuses.......
Both fuse boxes (in engine bay and on dash) need to be checked.......check all fuses visually, it would only take a few minutes.
Having checked these, and if everything is up to norm...........then the problem would most likely be a faulty body control module.....
That may be checked using a scan tool, or even replaced momentarily to confirm the fix.