If we take a progression like i III VII iv, does the absence of a raised leading tone mean we arent in a minor key? Are progressions like these "modal" progressions?
I only studied some classical theory but not medieval theory. Since you care about minor mode and chord progressions, I'll talk about the classical theory.
First of all, to establish a key in classical music, one needs to have reinforcing cadences. Composers may introduce additional notes to hint the key, but until enough reinforcement shows up, a key is ambiguous. So yes, i III VI iv alone doesn't give you a minor key.
You probably shouldn't even label the chords this way in the first place because you don't know what "key" it's in. It's just for communication so people know what kind of chords you're talking about.
As for whether they should be called "modal progressions", it really depends on what context you put them in. If you see a passage like this in classical music, and it never gives you any leading tone, it's probably just an ambiguous section, or part of a larger minor section. If it's an earlier music, well, you just don't label them with Roman numerals.
Yes, Aeolian - or Dorian - or Phrygian. All of which are minor modes - there is nothing that's a minor tonic - minor modes due to the m3 between tonic and 3rd.
The raised leading note came about centuries ago, mainly to make the V sound more like a dominant, leading to the tonic. It's not necessary to include it in any minor piece, it's just that it does get included, for reasons above.
Aeolian, Dorian and Phrygian may come under the 'minor key' banner for some, and under 'minor mode' for others. But a piece which uses A B C D E F and G only are certainly in minor modes, if not, for all, minor keys, all possessing the 'flattened' (or rather),'not raised' leading note. That aspect alone is not enough to prove something is 'in minor', in fact, it isn't even a criterion!