old 2006 Mac security has lapsed and can't use eBay or any shop platform

I'm surprised that your neighbor has not run into problems browsing the Web long before now.

The original form of https security was found to be insecure, and there was a concerted move to upgrade Web sites and browsers to use a stronger protocol. Modern https Web sites are likely to reject connections from any browser that only knows how to connect using the old protocol.

A 2006 iMac cannot run anything later than Snow Leopard (early/mid 2006 models) or Lion (late 2006 models).

The change to upgrade Safari to use the new security protocols first went into El Capitan, and I don't believe that it was ever back-ported to Snow Leopard or Lion.

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Another problem with using such old operating systems, and old versions of browsers, is that sites have evolved in other ways not directly related to security. An old browser may not be able to render pages from current Web sites well enough for those pages to be useful.

1. No
2. It is not real, which obviates the remainder of your questions except for:

Any other ways to update or solve this problem?

No browsers that can be installed and run on that Mac can be used for any recent websites requiring recent security protocols. Stated differently yes the Internet will work, but most websites won't. Most email services won't work either.

Websites that do not use encryption will load, such as http://www.gremlinx.com which illustrates the effective age of that Mac.

Unfortunately, modern internet requirements have forced the retirement of old computers, in terms of both secure and practical usage. For online business and financial transactions, continued use is too risky. It's a tough pill to swallow, but a computer that's almost 20-years-old has more than paid for itself.

As far as your friend having "the latest version" of Firefox, he is mistaken. The extended support release of Firefox 115 is intended for older Macs running Mac OS 10.12 - 10.14. Since every 2006 model iMac can't be updated to those OS versions, there is no supported version of Firefox that your friend can run.

From the Mozilla website:

When he first bought that Mac may seem like yesterday to him but he got couple of decades out of it. That's pretty good and a testament to how long Macs last in general. They are the least expensive computers to own, by far.

If the Mac were only ten years old, sure, it would still be usable. 19 years old... no. Buy him a new or refurbished Mac, and he'll get another decade out of that one.