How can one cusyomise thee home login page, to add information about the purpose of the site, inages, and so on - basiclly provide my own, wiht the loigin button fron the plain default?
I think a pinned topic as a banner does this job well 
But… if you still want to do it will depend on some factors
Do you have SSO or a Custom OAuth provider? You can customize that site in that case
Will you use Discourse’s default authentication? You might be interested in this plugin maybe:
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Maybe check the Brand header theme component or Versatile Banner.