In that case, I guess you will have to build those 2 features on your
own. For example, you can set up a proxy server to handle the cookie
authentication part, and have the Google Mini crawl via the proxy.
There may be an even easier approach, depending on how your website is
set up. For example, if the cookies are not dynamic, and do not
change over time, you can include the static cookie information in the
HTTP header. This will allow the website to recognize the Google Mini
as an authorized user, and allow it to crawl the content.
As for the suggestions feature, you will need to set up something,
perhaps on your web server, to offer the suggestions, and modify the
search frontends to receive and show them.