MacBook Air stolen recently. Can I re-install my purchased standalone LR5 onto a new laptop?

Question

I purchased a standalone version of LR5 in February of this year.My  MacBook Air was stolen a few days ago (so sad), and I want to know - can re-install LR5 onto a new laptop (I have the serial number and my previous laptop was the first installation)?
This is a side question that perhaps I need to post into another thread, but I have over 7000 photos backed up onto an external HD, many of which were edited, yet previously I had lost many of those edits when I retrieved the images from the ext HD. 
I have been managing my library outside of LR5 and only making LR5 aware of the location when I am editing a set, rather than importing into a main catalog inside of LR5. If the raw files are saved elsewhere (ext HD for example), then where is the non-destructive edit information saved, and should I be doing something different in the future in order to preserve the edits I have made? 
Typically, when I am finished with a set, I have been exporting them as full-sized jpegs, which I know are saved, but how do I keep from losing the edits that haven't been exported?
Thanks in advance...

Answer 1

Hayhill wrote:
I recently replaced a laptop. When I tried to activate Adobe CC it gave me a warning that CC was installed on 2 computers already, and a choice of going to one of the others and signing out, which I did, or singing out of both from that screen on Adobe's website. Point is that you should "sign out" of Adobe CC on the stolen computer so you still have another license to use and so the thief cannot use it. I am not entirely sure how to do that, but am sure there is a way.
Original post talked about purchasing the stand-alone version, so none of this applies.