Hi TiM, and welcome to PhpDig.net!
>> ...how to make not a pagesearch, but a sitesearch...
In the config.php file change NUMBER_OF_RESULTS_PER_SITE to one.
>> ...somehow index pages in both...
PhpDig currently supports just one single-byte charset.
>> ...use PhpDig for global Internet crawling...
PhpDig can be used to make a
smaller search engine.
>> ...PhpDig supports https...
PhpDig currently supports http but if enough demand https can be considered.