First, thanks for the great comments 🙂
To your question, you can use the theme installer for WordPress to install the Pro versions as well. The only thing you won’t be able to use is the theme search and install method like you can use for free themes from the wordpress.org site. For the Pro ones, you make the purchase from my site (or the theme membership), download the package, unzip it, then inside that is the theme zip file which is the one you can install using the installer from the admin.
Regarding settings… upgrading from the Lite to the Pro is not a direct upgrade and the Pro’s are considered separate themes. I’ve personally never tried replacing the existing Lite version of any theme of mine with a Pro version to see what happens, but if you do this, I strongly recommend you make a backup of your site database and at least, the theme before overwriting it (replacing it). The child theme will not work either, you will need to use the child theme specific to the theme being used because the child theme looks for the corresponding parent theme.
Ultimately, what others have done is install the pro, activate it, then update the theme options for the new version. Likewise, if you install the Pro, install the child theme too and use that, but again, the options will have to be reset for it. I know some people will simply redo the options and colours, but others will write down the options and then add them to the new version option settings.