Hi,
1. The smartsearch system will indeed index one product per category. so if you have products in several categories, you'll see the products several times, unless you also use the category filter (a dropdown) to filter further the results.
We actually have on our todo list the addition of an option to index products only once per category (loosing the category filtering in that case).
Regarding the way the search happens on the texts, you can't change these. It's handled by Joomla's smart search system (maybe Joomla has options for that ? but it's out of the control of HikaShop), HikaShop only provides the data to be indexed by Joomla's smartsearch.
2. Categories are not indexed. It would require the development of another smartsearch plugin and even if it would, you would get a category as a result, and then you could click on the category to get the listing of the products of that category.
We actually have such plugin for the normal search of Joomla.
I would recommend to look at using the normal search, together with such module:
extensions.joomla.org/extension/universal-ajax-live-search/
It allows for results as you type, like the smart search, but don't have one product per category and can also work on categories.
With the filtering system in HikaShop Business, you can have the results as you type too, but it won't search on the categories. You can however have dropdown filtering on categories, custom fields etc. The big advantage with the filtering system is that you get the results displayed as a normal products listing so it's much nicer than the search results from the default view of Joomla.