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Been watching sgdq and agdq for a while now finally decided to give this a try if I can get my software working right, wanted to try a run of Yu-gi-oh duelist of the roses. wasn't sure on a few things

1. Is it fine to play on an emulator? or do I need to bust out a ps2
2. after completing half of the game it gives you passwords to get a different card, just another part of the game, would it be fine to start the game and immediately use a password? Don't really skip anything so I'd assume it was fine just wanted to make sure
Thread title:  
Dapper as fuck.
The main thing about 1 and 2 is to find out from the actual community specifically for your game.  You might see if there's a specific thread for that YGO game on here, or you can find out who speedruns it and ask around.

If you want to submit to SDA, you cannot use an Emulator by and large.  They only accept a few, and they are generally "official" ones like Wii/Wii-U VC.  They pretty much never accept emulators to play the game on your PC instead of original hardware.  However, if the community itself accepts times on emulator, they'll know what ones they accept. 
Edit history:
Zergreenone: 2016-06-19 04:01:20 pm
Zergreenone: 2016-06-19 04:00:48 pm
Zergreenone: 2016-06-19 03:58:49 pm
Your second question would traditionally make your speedrun NG+, or New Game Plus, which is where you have completed the game already and thus have a save file/save code and extra bonuses but you are still starting a new game.

The first question is generally no, unless the emulator is officially supported by the makers of the original hardware, or there is good reason why you cannot use the original hardware.

As previously stated, both answers are subject to community decision.
A better answer is that you can do what you want. It's your enjoyment. There's no legal entity governing speedruns .
Now, if they are accepted on the loaderboards is a case by case basis, and as others said submitting runs to SDA must be official releases.