Are there any limits as to which emulators are allowed or if emulated runs are allowed, or if there are any limitations on how fast emulated runs are allowed (basically, if I get a fast time on emulator, would it be rejected vis-a-vi Super Mario Bros. where they only accept emulator runs that are a percentage slower than the current record runs)? Thanks in advance for the help!

As far as I know, all emulators are allowed that are under the drop down menu for submission. Frame rates should be close to 60 fps to mirror the NES. What kind of frame rate is your emulator putting out and what emulator is it?

I currently use NEStopia UE vx.xx according to the emulator's about page. What I meant by "fast" in my original post was when I start running this game, and I start out with times that are fairly fast and or improve my PBs quickly, what I was wondering is if emulated runs get rejected due to being too close to the WR run (not that I'm going to get there anytime soon.)

I started with Nestopia when I joined the community. So there is no issue there. You will find a timing delay between your pressing the button and samus action on screen with the emulator. With original hardware and a crt there is no delay. But your runs won't be rejected just because they are an emulator.