What does the (Awesome!) next to save file names mean? Is it just for funsies?

the more you save the less awesome you get.

Yes. For some weird reason developers decided to discourage frequent saving. Nothing bad happens if you do, however you get worse and worse save tags the higher the count of saves within a particular level is.

It's a simple but surprisingly effective method, I have to say. I found myself trying not to save too often just because of that.

I didn't save for and hour and a half because I couldn't find the save menu. Glad I finally found it because I'm willing to bet the game gets more deadly past the first level.

Well, it's complicated. The game of course gets harder with time. But your character becomes stronger, you gain access to more powerful combos, and you also get better yourself. So you are actually more likely to have trouble in the early levels.

It's been many years since I played it (used the Dwarf back then, now I've started again with the Knight) but I seem to remember having generally less trouble with the combat after hitting the halfway point or so. On the other hand, the platforming never gets better, in fact it gets worse, so it would still be a good idea to save once in a while, especially before risky jumps.

If you save only twice per level you get to keep your "awesome" tag. You can even upgrade the tag if you manage entire level without saving.

My lowest number of saves is 48. That puts me squarely in Heroic territory (between 29 and 70 saves), but nowhere near Awesome.

Judging from the achievements list, that seems the most common result so far. I guess even if you save a lot, you are unlikely to go past Bold (129 saves means almost 10 saves per level).