1. Make sure when you install the CC version that you choose the Advanced Options link in the installation dialogue window so you can turn off "Remove Older Versions". CS5 and CC will coexist on your hard drive without issue. It would likely be much better for your stress levels if you kept the old version while learning the new, a lot has changed. Depending on your ability to work with code, you may find the new DW difficult to work with out of the gates.
2. I don't think the old sites will transfer automatically from CS5 to CC2017. I'm not 100% sure about that, to be safe, it's a simple process to export your settings (under Site > Manage Sites > Export) into .ste files. Those files are just the site settings, like FTP or local testing servers, not the html, css or js files themselves. You would then go to Site > Manage Sites > Import in DWCC2017 to bring those site settings across. There's no need to do anything with the site's files, unless you're also moving to a new machine.
3. Like I mentioned above, things have changed in DW. Any features you were used to in CS5 that don't exist in CC2017 (like "anything Spry" for example) will need to have its code edited manually. The old dialogue windows for editing in the old features no longer exist. Keeping your old version around until you update your site past those old features will work though. You can have those old versions installed on the same machine, they just won't run at the same time. So to edit in an old feature, close CC2017 and open CS5 make your changes, save, close and open the new version to use new features.
3b. As a CC subscriber, you will have access to all CC versions of a given program. With DW, you have CS6 Cloud, CC, CC2014, CC2015 and CC2017. Each one can be installed on your machine in order to use various features, if you like. For example, CC2015 is the last version of the program with Fluid Grid support, if you had a site built on Adobe's old FGL, you could use that version rather than CC2017, which drops support for them.