So, is a re-written or strongly edited work an original one?
Almost certainly not.
The reason publishers care about first rights is that very few people are going to buy a book they've already read.
By putting something on the Internet, you're effectively exercising your worldwide first rights -- anyone anywhere can read it, after all.
There can be a lot of differences and improvements between the first draft of a novel and the final version that goes to print (or e-print), but most of the time they're clearly the same basic book. Unless you make very extensive changes, I doubt that publishers will be very happy with you. If the two versions of the story were written by different authors, could one of them plausibly sue the other for copyright infringement? If a reader read both, would they go 'hang on, I've seen this before...'?
If you want critique, you should be fine posting your stuff on closed writing forums (I'm pretty sure we've got a list of some of those on this site somewhere), or you could find a writing group in your meatspace location (I would 100% recommend this). If you want to 'test the waters', you should be safe putting the first few chapters of your novel online and maybe starting a blog discussing worldbuilding type stuff.
But if you post your whole manuscript online, expect to be rejected out of hand by publishers.
(There are exceptions, of course, but you probably aren't the writer of the next Fifty Shades of Grey.)