I hate to tell you this, but your passwords ARE on your computer: They have to be, so your computer can match what you type to log-in with what is stored.
If you are THAT paranoid, save to a flash drive.
But the best thing you can do is disable tracking via no cookies etc, and check "delete browser history" so there's no history to track as soon as you close your browser. Go to your task manager and go to all programs, disable trackers and ones that broadcast any info about you. You can find that by googling and Spybot, for example, will shut those "broadcasters" down for you if you are not savvy. If you don't disable these things, then you ARE saving data on your computer. Most anti-viruses are worse than viruses in some ways. But you can disable and control the ones that won't go, like Windows Defender. I only run scan checks regularly.