"Some of these suggestions need more thought on my side, for example, if I can find a clever way to better distinguish cavalry from horse archers." => I suggest you to have clearly different horse color, this will help.
"I'm not sure what you meant by "hard to select units" without having seen a video. I saw something similar in a gameplay video and already made some changes to better select units on tiles." => simply hard to click on the model when the game is zoomed out
"And if I understand you correctly, the third characteristic in the UI, besides health and damage, is the hotkey to quickly spawn the unit." => it was for me not that clear, because for the units (not building), it was like a number. Now it is clear, thanks.
"I also like the idea that units that died inside the round will only reset the population counter after the round ends. Although I am pretty sure that some players might think that's a bug if not explained well." maybe you can indicate this in the UI through a small skull and a number near the limit.
"Aside from your suggestions, have you encountered any bugs or glitches or just things that don't make sense?" => well I some situation where I was not able to find why a game did not ended properly although I kicked all the other people, and their buildings. I assume there was a mine I didn't found, although I looked thoroughly.
Looking forward for the next update.