For things like the auth process and validating a user there shouldn’t be too many changes. The most significant change from v3 to v5 if you’re using any other endpoints is that any requests that use the username in the URL path instead use the users ID in v5. So for example if you used https://api.twitch.tv/kraken/streams/SomeUsername you would instead use https://api.twitch.tv/kraken/streams/123456 in v5.
Correct, v5 is deprecated but no removal date yet. As Helix (the new API) is still in development this means that v5 will continue to be supported until Helix has feature parity with v5, at which point they will start giving out warnings and plans for removal (this likely wont be until the 2nd half of 2020 based on how long v3 has taken to be removed).
A developer account should let you get emailed about important changes, but I also suggest going to the Announcements section of these forums https://staging-discuss.dev.twitch.com/c/announcements and just to the right of the ‘New Topic’ button is a notification button which you can toggle to give you notifications any time there is a new thread.
Any major updates will also likely be mentioned on https://blog.twitch.tv/ but that’ll most likely link back to these forums anyway but that’s another option to monitor for news.