To help you best we need to know the model and year of your Mac, and the version of macOS it is running.
Find that info by clicking the Apple menu () at the top-left of your screen and then select About This Mac.
(Note- for privacy and security please never post your serial number.)
If you are having trouble connecting to and using websites with your older version of Safari, try it with a newer third party browser that is still being updated to meet current internet security protocols.
I suggest you take a look at Firefox browser or Brave browser.
Download an alternative browser and install it into your Applications folder. Launch and use that when you encounter websites that don't play well with Safari.