How can I ensure that DaVinci Resolve will detect and/or load my .mp4 / .avi files?
From your post I am not sure why Resolve wont recognize your files...but you should transcode your footage anyways before ingesting into Resolve. 

Even if you start with highly compressed source media, you should transcode to something less compressed, and that will put you in 4:2:2 at least vs working with 4:0:0. ProRes or DNxHD codec will give you files that are much less compressed, and will yield the best possible results in color correction.