Natalie,
First off, I'm going to move this topic to the JFBConnect 2.5 forums after I post this (instead of the JLinked forums), so please look for it there.
As to your question, JFBConnect has many settings for automatically logging the user in or not after registration. If you have Joomla activation enabled, for instance, JFBConnect allows you to skip that. If you don't, the user will not be logged in automatically, since they need to activate first. If you choose to skip it, they should be logged in immediately. Similarly, there are multiple registration settings for automatically creating the user (no forms) or letting the user pick their username/password, etc.
We've heard from quite a few users that are using Hikashop and JFBConnect. To our knowledge, the two work fine together, but it's not something we directly test.
As always, we have a 30-day money back guarantee and provide excellent support. Should you run into issues, we'll help how we can and if you are satisfied, no worries
Hope that helps explain, and best of luck,
Alex