Your rating of the outsider CR is incomplete since you have omitted its attacks/damage.
No. Attacks and damage are not already factored into Outsider HD! (This is an incorrect assumption you have made).
BAB IS factored into Outsider HD (and indeed all monster HDs) but NOT their attacks, nor their damage.
eg. Dragons get Fighter BAB, BUT THEY DON'T GET A FIGHTERS ITERITIVE ATTACKS!
You don't. The problem you have is that you have not added the 20HD Outsiders attacks/damage to its CR. Hence the reason you are getting incorrect results when juxtaposing your Outsider and a 20th-level Fighter.
No. What I said was it was set up to facilitate CRs.
You could easily break down Hill Giants or other monsters as Class Levels using my rules, but thats simply not something I am going to do for you. I only have limited time and space. This CR/EL system is an appendices to the Immortals Handbook, not the other way around...although given the time expended on the bloody thing lately you could be forgiven for thinking otherwise.
You don't. What you do is remember to add the Attacks/Damage CR factor to your Outsider. That then gives you the proper CR.