Sadly Lion 10.7.5 is the last version of OS-X this system can run. Nothing newer is supported and will be even slower if you fudge it!
Between its older 32bit architecture and lack of supporting more than 4 MB of RAM and a slow 1.5 Gb/s SATA I drive interface it just can't support what modern OS's & Apps need today.
Your problems are related to how the Web has moved on to newer methods of rendering graphics which your current version of Safari can't understand.
This is also true for other older web browsers. Many today don't even offer 32bit services which is what is also hitting you as the app developers have taken 32bit services out of the code so these apps won't work on your system at all.
In addition Apple has long since stopped supporting both the hardware & OS so any security weakness they have can and ARE! Leveraged. So any site you visit can have a rogue worm that even the site owner doesn't even know it there!
Time to put this poor beast to pasture it served you well for many years.