There are two different issues at play here...
The first is what chrome, gmail, etc do with files they cannot open directly... examples being that they generally know how to handle a few types such as pdf files, but don't know how to handle others such as gpx files used in mapping programs.
These "unknown" file types are simply downloaded to the "download" directory, and the second issue is selecting and setting the app that will open them when you access the file in the download directory. Android has some major gaps when it is confronted by many "standard" filename extensions.
When "Advanced Download Manager" is running and a file is downloaded, it intercepts the download and handles these issues without user input based on the filename extension and configuration by the user. Not perfect, and it takes some experimenting to learn the interface, but it works.
...for example, downloading an mp3 files to a specific directory then setting a default audio app when the download is finished by tapping the file in ADM's "finished" column.
You can set different download directories for each file type at the beginning of each download and set that directory as the default destination
Then, when you select the "finished" tab and tap the download, you can choose which app to open the file (as usual, "once or always")
Like everything tech, it ain't perfect but it's much better than the default handling of many file types.
As for your "partial download" query, insufficient data cap'tn Could it be that the free version has a size limit?
Hope that this clarifies, at least a bit.
Beverly Howard