Under-sink Wiring Help (for Disposal) - Made a Stupid Mistake; Now Concerned on Safety

[justin494]

Goal:
Wire Garbage Disposal (Unit = https://goo.gl/Ucwzq).

SEE STEP 4 OF THE MANUAL FOR WIRING INSTRUCTIONS

Current Status:
Completed and wired but I'm nervous.

I'm kicking myself because I went too fast and I failed to follow instructions. I cut the head off the power cord, which the manual specifically says not to do.

Power Source:
Romex directly from 20-Amp Breaker (a pro put the wiring in place for a dishwasher and I'm trying to tap in)

MS Paint Diagram:
http://imgur.com/a/v2yp7

Photo:
http://imgur.com/a/mG4AC

Questions:

1. Despite warnings in manual, am I ok to cut off power cord's head?
2. If yes to #1, am I ok to assume ribbed black = white
3. Am I ok to join the dishwasher and disposal together within a single wiring nut like this? Will there be too much current (especially concerned whether the current from the dishwasher will overheat the flimsy garbage disposal "power cord")?
4. Am I properly grounded even without using "BX" cable? The manual seems to imply non-BX cable means I need to ground to a pipe?
5. In general, is this setup 100% safe? I'd much rather be safe than sorry.
6. Given my mistake (see #1), how can I salvage this?

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ALSO NOTE:

• The switch is a 15-amp switch, I'm going to upgrade to a 20-amp switch to match the breaker.
• For lack of a better term, I plan to jam all of the wiring nuts into a plastic gang box like this: https://goo.gl/T6HOxK

 

[justin494]

After some feedback from another forum, I'm now thinking something like this would be better:

http://imgur.com/a/N16YB

I don't know how to delete my post but I'll leave this here. Thanks for your time.