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Some people do subdomains (like you've outlined above), and some do directories, i.e. mysite.com/en/, mysite.com/de/, mysite.com/fr/.  It used to be recommended that you do directories, as they keep your domain authority pooled better, since subdomains each have their own concept of domain authority.  That seems to be less true today, so I'd do whatever is easier for you to set up.  All else equal, I'd opt for the directory structure.

Hi, I would use 301 redirects from the old pages to the specific pages of the new domain.  Make sure you redirect a page about rome A from the old domain to a page about rome A on the new domain.  The page on the new domain should be something similar to the page you are redirecting so that when visitors visit the old domain and get redirected to the new domain, they will still find what they are looking for. Although your new domain does'nt have much authority but with 301 redirects, it will redirects 99% of its link juice and authority to the new domain.  So 301 redirect will help a bit with the new domain's authority. in conclusion, your first plan will work. Hope this helps.