Sorry for not responding earlier, I was asleep during that time. To clear a few things, yes, the launcher connects to minecraft's login system with one special exception of the "Play Offline" button which bypasses said system and logs in the player as a cracked user. The launcher also does not and will not ever store a user's login details to any file in the server. I checked the relevant core code again of the launcher which deals with logins and I couldn't find any file log system of user ID's and passwords.
About the anti-virus issue, unfortunately it's because all .exe and .jar files in most browsers will be treated as suspicious programs unless they meet certain requirements, either we buy a digital certificate costing well over hundreds of dollars, or if the file has been downloaded over tens of thousands of times, or if the file has been downloaded from a trusted website. I'm not exactly sure what the third requirement is but it would be something related to a SSL certificate for the main hub page.
Try to login the launcher using your email and password instead of your name and password. Maybe try to close the launcher, restart your router and launch the launcher again. I can't recommend a concrete way to fix this since this has been the first time hearing about such an issue. Let us know how everything is going on your end. Thanks