Thanks for your request. Currently it is not possible to include a keyword search directly on a page. That would be very imprecise anyway, because you would have no control over the resulting products. But you could use the search page import function of ASA2. It is described here: http://docs.getasa2.com/import_url_importer.html#search-result-url
This feature gives you control over which products you want to import into ASA2’s product repository. You can then add categories and tags to the imported products as you are used to in WordPress and then use the extensive filters of the asa2_smart_collection shortcode to display the products you want. Here you find the filter options for smart collections: Here you find the filter options of the shortcode: http://docs.getasa2.com/shortcodes_asa2_smart_collection.html
I hope I was able to help you. If you still have questions, please let me know.