The new user interface ("64bit") version was first released by Pitney Bowes in 2014, MapInfo Pro 12.5. Pitney Bowes then released a compatible Discover add in version in 2015. The Discover addin (not MapInfo Pro) was sold to Datamine in 2017.
Note it is not recommended or supported to do this, as some workspaces and files are not backwards compatible and it is End of Life and no longer supported.
Yes you can! It does not require a separate license. It does not matter which order you install the 32bit or 64bit.
Download links are here -