Questions Regarding PS1 Emulation on PSP?

I'm planning on getting a SD card to memory stick adapter for my PSP so that I can play downloaded ISOs on it. I also plan to use it to play emulated PS1 games that ARE NOT from Sony.

With that taken into consideration, I'm interested in a PS1 emulator for PSP with the following specifications:

1. Are there any PS1 emulators for PSP that are better than Sony's official emulator? If so, in what ways?

2. Does the PS1 emulator offer video output? For me, this is a make or break deal. If it does offer video output, does it support resolutions like 240p and 480i? Is the video output quality any better than Sony's emulator? (I.E. less dithering and less jumpiness when changing between 240p and 480i?)

3. What controller options are there? Do certain emulators offer custom button assignments too?

4. What unique options do these emulators wield?

Thanks!

Yes, there are lots of ps1 emulators for psp. Sony's official emulator is not so reliable. But choosing the best emulator is difficult task. Here is full detailed article that you should read to get best ps1 emulator for you psp.
The answer to the second question is that yes ps1 emulator offer video output but some emulators don't offer video output so you need to choose best for you.
Answer to 3rd question is while there's an option of remapping the controls however you want, generally, you'll assign either the R2/L2 buttons or R1/L1 buttons to a D-pad press or one of the directions on the analog stick (depending on which control scheme you've chosen). If you have a PSP Go synced with a DS3/Sixaxis, it will use all the buttons correctly, which is great if you're outputting to a TV.
To get answer of your 4rth question, you must see this video:
https://www.youtube.com/watch?v=kxMH67yvEqo