1. Updating the code isn't necessary to work with code from older versions of the program, however, you may not have the same dialogue windows you were used to, if a feature has been removed from DW in the latest incarnation.
2. DW will not auto-update code. It will generally plug along, allowing you to use whatever code you like. Though it is more susceptible to crashing or doing odd things when it runs into actual code errors.
3. If you have a website that is vulnerable to things like code injection, new versions of DW will not fix that. Some of DW's old server behavior functionality has been described as "less secure", but then, so is everything made 10 years ago when you talk about the internet in general.
The old perpetual license version of CS6 can sometimes have its start-up taken over by the CC Desktop App (where there was also a CS6 Cloud version) and effectively stick you with a non-working program until the older one is reinstalled. If you run into issues, a reinstall of the old software will generally get you up and running again.