Re: buying software online
a & b) you get a serial number and a download link. if you have to reinstall it, you re-download it and reauthorize it.
c) some don't, some do. some don't seem to care about installations, the theory/practice being that you are only authorized to use one copy at a time. others provide you a software authorization key when you install the app. the key is specifically for the computer you are installing on so the company then knows what computer (and how many) the stuff is installed on. native instruments komplete 2 works this way; i can only have it installed on 2 computers at a time. if i want to install on a third computer i have to first de-authorize one of the other computers. despite maybe being a little limiting, it actually all works very well.
and then some other companies give you hardware usb dongles, coded to the app you bought. the app won't run without the dongle. but this is generally only applicable for off the shelf software.