Is home website hosting feasible with a home server delivering a site to the world over a broadband connection?

Technically yes but  home website hosting is really only something for hobbyists at one end of the scale and major companies with their own data center at the other.
There are numerous top website hosting companies who will host your site on their servers for a small fee and they will take care of the all maintenance, security and resilience issues, as well as providing support.
The only practical reason for home website hosting is to learn how to do so and to understand the issues. It will not save time, provide a better service or save money.
If you still wanted to go ahead with home website hosting you would need to consider the following:

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