desu vs da vs de aru vs de arimasu

OK. I'm lost.

Question 1:
In increasing degrees of politeness, what is the order of だ、 です、 で有る、 で有ります ?

Question 2:
Why would someone want to use で有る instead of で有ります? Same goes for いらっしゃる and いらっしゃいます.

Thanks for clearing this up!

である is virtually never used by itself, but it can be used in certain verbal forms which can't be formed with だ or です. For example, です does not have a ば conditional form, so if you want to say "if it is X" with the nuance expressed by the ば conditional (as opposed to たら or と), you say Xであれば.

I think であります is similarly rarely used. However, the super duper polite form でございます is sometimes used by shop clerks to customers or similar situations where such polite language is used.

Thanks for the help!