1. The "Search by Name or Category" with the additional categories is missing, and so I can't easily search most points of interest outside of the other 4 categories...
Is there another setting that enables the "Search by Name or Category" options in Luna?
Just start writing...

Spoiler: IMG
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2. Is there a way to change the amount of places listed in each category? In NextGen it was a maximus of 100 places, but there are 20 shown at maximum in Luna.
Changing this to 100 does not help unfortunately:
Try this...

[poi]
search_max_result=100
search_global_area=200000
search_route_area=1500
search_help_area=50000