Do the most popular BYOND games come up with their own original icons, or is it more common to "borrow" them from elsewhere? If they are original, how do they go about creating such good-looking icons? How do you make your game LOOK attractive to players?
Umm I would say it depends on the game. But I would hope good games have original icons. Now for creating "good-looking icons", that's just practice and learning how to make them. There are tons of tutorials showing you how to, and examples via existing pixel art if you are stuck on how to shade something. Some players may not like the art style that is being used, which is completely fine.
Do you think making graphics is fun and worth your time? Or do you hate it and feel like it's a chore that you just have to do to make your game original?

As a player I care more about how fun the game is. I don't really care if people use free art resources (as long as they are actually free or properly paid for). Some people will judge the visuals more than me but even then, whether you drew everything yourself won't matter to most people, just whether it looks nice overall.

Furthermore, you can always use placeholder icons in the earlier stages of development, and then decide later to change them. But you can't use placeholder code! So my point is, make a fun game first, worry about the graphics later!