I'll have to see if we can rename this forum. No sense having it be version specific.
1. Yep; you can see all the commands with a core.help. I poked into the software manager and there's a 5.0 and 5.1 API guide doc posted under both ePO versions, and the sizes are different but a cursory peek doesn't show a 'what's new' section or anything like that.
2. Generally yes; there may have been a few changes or tweaks but should be additive.
3. There's a Web API guide posted in the software manager underneath Management Solutions => ePO 4.6/5.0/5.1. It should be posted on the download site as well but it's easiest to grab from the sw manager imho.