Websites (2) integrated into 1 domain

i have a website that is basically 2 websites withe 2 different wordpress installations on 2 different domains using 2 different themes, i would like to merge the 2 together so i have just one site. the issue is i have plugins that work on the theme of site 2 but do not work when installed on site1. site 1 is the new theme i have made and the one i want to use moving forward. So i need to integrate the plugins and the pages into the new theme which is ocean WP. so the login pages my account pages, dashboard etc all need to be integrated from shapely theme and made to work in the ocean WP theme.

i would like the header and footer to still be the same and work fine
i would like the login page to look a bit more professional
i would like to remove the sliding sidebar menu and be able to set this from the menus admin tab
i would like the confirmation pop up up buttons to look better than the standard default ones
and to keep the size of the site as small as possible