Yes. Absolutely, yes. The fact that the program is quite simple, in my opinion, makes it even more attractive to re-program it from scratch, because it's a less risky, less time-consuming proposition, and the rewards are still the same. Definitely, absolutely, 100% re-code.
None whatsoever. I (and many others here) have a System Integrator's license - this means that we pay an (exorbitant) annual fee and in return get a year's activation for every single software product Rockwell make. I have literally hundreds and hundreds of Rockwell software licenses on my activation server, and they all play together just fine.
If you were talking about installing, say, Siemens software on your Rockwell machine, then I'd urge caution for those reasons. But there is no way an RSLogix 500 license will negatively affect an RSLogix 5000/Studio 5000 activation.
You can export the documentation to an .EAS file from RSLogix 500. It will take a bit of poking and prodding, you won't be able to *directly* copy/paste into your RSL5000 CSV file, but it's doable.
The registers are for the most part pre-defined in RSLogix 500. B3 is the array for Boolean data - so B3:1/0 means "data file B3, word 1, bit 0". Likewise, N7 is the default register for 16-bit integer data. So N7:14 means "Data file N7, word 14". In both B3 and N7, you can address the whole word or individual bits - e.g., you can address B3:3 as a whole 16-bit word, or you can address N7:8/12 and get just bit 12 of word 8. Which begs the question, why bother with two different data types at all, but that's a different tangent.
You can then add more registers of any type you want. So maybe I'll create N19 for all of my integers to do with a certain task, or a certain part of the machine. Maybe I'll create a new register of timers, called T11, to stick all my alarm timers in. At the end of the day it really doesn't matter if you're converting to RSLogix 5000, but you'll probably find as you get into it that all of the B16 elements are somehow related, as are all of the B18 elements, etc.
This is something you'll have to look into a little deeper. RSLogix 5000 does not have the same status bits that RSLogix 500 has. For each status bit you find, you will have to dig a little deeper into what that status bit actually does, and then try to work out the equivalent function in RSLogix 5000. One exception is the first scan bit - I *think* from memory in RSLogix 500 it's S:1/15, and RSLogix 5000 does have a direct equivalent - S:FS. A good starting point to delve into the others is the GSV instruction - have a read up about that and you'll get some idea on how the platforms differ. For any other curly ones, if google doesn't help you, post them up and someone will steer you in the right direction.
Other than the fact that "ETO" is "OTE" in reverse, and "OTE is a standard "coil" output instruction, I have no idea. That's almost certainly coincidence. If it's just part of the tag name/description, it has nothing at all to do with the programming techniques you'll need to employ.