Keigo Help!

[ichigochoco]

is ご機嫌いかがでございますか。 keigo for お元気ですか

is this grammatically correct? なぜでございますか。 (i'm trying to say doushite in keigo form but it sounds weird. Would naze be honorific enough?)

まだけいさつをつかまらなくてよかったでございます。for its a good thing the cops have not (graciously) caught you yet. or should it be まだけいさつがおつかまいになくてよっかたでっす。 or are both wrong?

And the rest, I'm not sure if I made a mistake
つかまってしまいました
せいぎのみかたなので、 つかまらないはずでございました。 or is it おつかまえになれないはずです

[TrueNappa]

is ご機嫌いかがでございますか。 keigo for お元気ですか

is this grammatically correct? なぜでございますか。 (i'm trying to say doushite in keigo form but it sounds weird. Would naze be honorific enough?)

Ooh... I get confused with Keigo, too; but, I think that the でございます takes the phrase a little too polite-overboard. I know there is the phrase ご機嫌いかがですか。 which is already very polite and an equivalent of お元気ですか。

If you add in でございます, I think you could inadvertently make the phrase sound sarcastic; like, a "oh and how are you doing, your majesty of a friend/professor/etc."