I got into speedrunning about 5 months ago and I personally enjoy it, even with the struggles.. A few issue have been on my mind though, such as proper setup and equipment. I don't have a PC, so I can't stream or display my time. I have discovered ways around this, such as using a phone for timing, but then I have no way of automatically splitting segments, as it is only possible on pc. I also can't film the speedrun while also timing the run.
For my speedrun, I'm using an NES Classic Edition with a Super NES Classic controller, I was also wondering if these were allowed under the requirements, as I'm using a different controller. To my knowledge the only banned controllers are Turbo controllers, but I may be wrong...
I look forward to any helpful responses!

As long as you have your live game play filmed you're legal to submit. A camera recording your screen may not be ideal but it works.

You can use any controller, so long as it doesn't give you any advantage in any way over the original nes controller

With regard to splits. You don't HAVE to split, although it can be useful for your benefit. Without a pc in not aware of a way to do this. But it's honestly not really useful until you get close to the 5 minute mark anyway (for the purpose of predicting otherwise "random" behavior)

Good luck!

I was also wondering if a timer is absolutely required to submit a run, or is it more of a personal tool? I know you guys check through and time anyway. Timing my run with a timer onscreen would be hard because I can't start the timer right as Mario starts moving, and right as he hits the hammer. If a timer is required, I'm sure I could figure it out. Thanks for the help anyway!

I was also wondering if a timer is absolutely required to submit a run, or is it more of a personal tool? I know you guys check through and time anyway. Timing my run with a timer onscreen would be hard because I can't start the timer right as Mario starts moving, and right as he hits the hammer. If a timer is required, I'm sure I could figure it out. Thanks for the help anyway!

Timers aren't necessary at all for runs, don't worry about it

You don’t need much to submit a run. Taven’s former world record (4:55.746) was recorded by filming a crt with an iPhone SE without using splits. As long as you can see Mario jumping and basic stuff on the screen, you’ll be fine.