My iMac is 11 years old can it be upgraded or is replacement necessary?

It depends on what you mean by "incompatible" and what version of OS X you're running. 2010 iMacs should be able to run High Sierra, I believe, which would still be compatible with 99% of the web. I would upgrade your operating system first if you can (instructions here), and if you're still having trouble, try another browser like Firefox.

MacOS 10.12 is/should still be compatible with most (if not all websites). If your iMac is working fine for the most part, then consider using a 3rd-party browser like Firefox and/or Chrome. Assuming you're on a 2010 iMac, it appears you can upgade to MacOS 10.13 (High Sierra) which I recommend you do anyways and see if that resolves your problem. You should always be on the most current release that your iMac is compatible with.

Good advice above. Beyond that, I would not spend money on an old Mac. It could now fail at any time, so be sure to have everything backed up. I would look at getting a new Mac if that is possible.

If the problem is Safari is too outdated just switch to a different browser such as Firefix, Opra, or Brave. All of those are compatible with 10.12 for their latest releases.