Just to make sure that I sort of get it, since, not knowing any better and sort of reaching for any comparative, for a while I'd regarded adjectives 'erste' - 'zweite' - 'dritte' in the same vein as demonstrative dieser, jener, solcher etc. Not so?!? Two different animals ?!? :) What I mean is: "Dieser Schluessel ist gruen." vs. "Der zweite Schluessel..." I am going to sound like an idiot, but is nom. "zweite" always "zweite" no matter what gender is assigned to the noun?!? "Zweite Orange" and "Zweite Schluessel" and "Zweite Zimmer" ?!? I had tried Christian's link below, but failed to find this particular point. My my...
This page clearly explains that ordinal numbers decline in the same way as adjectives (i.e. they can have different endings): http://www.germanveryeasy.com/numbers-in-german#declension-of-ordinal-numbers
Your link does not work. I found a better way to find the endings of adjectives. Suprisingly I have never seen this in discussions about inflections. In the book WIE GEHT'S by Sevin and Sevin there is no mention of confusing inflections. Instead they propose to use this rule: Except the obvious and memorable cases, if definite or indefinite article does not show the gender of the noun or there is no article at all then the adjective should show it otherwise there is only one ending -e. As in the above example der shows the gender of Schlussel therefore zweit end with -e.
I think it works in all cases. With definite and indefinite articles in dative and genitive cases there is only one ending -en (it is also the ending for plural in all cases). We can memorize this. Without any article the adjective takes the ending of the missing article. In accusative the rule also works, except masculine accusative where both the article and adjective end with -en and show the gender of the word. At least this rule helps to avoid 99% of ending errors and not be in the situation of brilliant soviet physicist Frenkel who said after his physics seminar in german full of article and adjective errors: It is germans who are responsible for these errors not me, why on earth they ascribe gender to inanimate things?
I think I agree with Frenkel, I also found this link that makes it easier to inflect adjectives: http://www.nthuleen.com/teach/grammar/adjektivendungenexpl.html