How to best manage to have two different WP (WordPress) sites on the same host

sorry for been so ignorant.
My case is:

  1. I purchased a domain (say domain1.site) and a host plan for this domain (with no sharing domain capability, i.e. the cheap one).
  2. Later I purchased another domain (say domain2.site). Now they asked for almost $300 in order to upgrade my hosting plan and make it able to co-host the second (or more? I do not care) domail(s).
  3. What is the best way, if any, without upgrading my host plan, to have two different WP installations responding to these web addresses (say domain1.site and domain2.site)?
  4. I know it is possible to have two WP sites hosted under one domain (in my case, say domain1.site). Then, the names would be something like: domain1.site and domain1/something.site? In that case there is no use for the second domain, is that right?
  5. Is it possible to alias the site physically under subfolders (domain1/something.site) to another domain (say domain2.site)? I think not, but need a verification.
  6. What about WP multisites? Is it relevant or can be of some help (concerning the two domain names)?

Many thanks,
Nikos.