Fossapup was released in 2020 and has no security updates of any kind. If you install it now, you're installing an OS with 4 years of known vulnerabilities, many of them with ready made exploits that can be found online easily.
The problems with browsers probably happen because the clock is not set correctly, or because Fossapup has 4y old CA certificates: it's likely that some certificates are expired, revoked or missing.
If you tell us what led you to it and not a more recent Puppy release, maybe we can fix it. puppylinux.com no longer offers Fossapup in the main page.