Sure, POIs are searchable. I added 300 POIs from my company, and could search on various categories. It all comes down to what custom fields you create for your POIs, and how you make your search form. The search form is plain HTML, so with a little HTML experience you can make it what you want.

Have a look at the search form for Hotels, that often has a bit more detail in the search form (and in the IDX file)

There's nothing to stop you looking for POIs with radius n, with name starting with letter X, or with any other category that you add to the IDX index file.

Remember: the search happens on the IDX file. The search results are then displayed from the URL file. So any custom categories have to be added to the IDX file.

If your search form is returning no results, then there is a mismatch between the fields used in the search form and the fields that exist in the IDX file

As for POIs on route - that's a limitation of the BMW nav. It searches for POIs within a radius of your position, not along the route.