- Well they should be same, specially when you are going to use Backup/Restore of site or Import/Export. If you are just going to prepare a WSP solution and use that in different environments, it should work but there maybe complications. Safe side, they should be same versions.
- You have two options: 1- Either you use External Content Types, External Lists and do it SharePoint way. 2- You can create Visual Web Parts and call these programmatically, not SharePoint way rather developer way. We personally prefer 2nd way because it much flexible.
- SharePoint by default works with Active Directory authentication but you can write your own Authentication Providers too. Maybe configuring Single Sign-On will make single user work for both ERP and SharePoint but I don't have much experience on this topic.
All of the above are opinion-based answers and it's my personal experience/opinion. You absolutely have the right to agree/disagree :)