Of your two questions, @istrasci's suggested link in the comments should address your first question, about collocation with ございます.
The second question is more about spelling conventions and morphology. The linked post doesn't quite get into this, so I'll address that here.
If とう [as an adverbial ending] is a monolithic morphological unit, why does a break occur in the kanji representation between と and う?
Your question contains within it the seeds of the ansswer.
The key is that ～とう is not entirely a monolithic morphological unit. It looks like one, but it is not treated as one.
Origins of the ～とう ending
As you describe, the ～とう ending is "an ウ音便 of たい". This ウ音便【おんびん】 is basically a matter of dropping the //k// from adverbial ending ～く, and then adjusting the corresponding vowel + vowel in ways that mirror historical sound shifts.
Note: The elision (removal) of that medial //k// is also what gives us the modern ～い attributive and terminal / predicative endings for so-called -i adjectives: in Classical Japanese and earlier, the attributive form for these adjectives ended in ～き instead.
Vowel fusion
The vowels fuse as follows:
- あ + う → おう
Examples:
- あらがたい → ありがたく → ありがたう → ありがとう
- おめでたい → おめでたく → おめでたう → おめでとう
- い + う → ゆう
Examples:
- よろしい → よろしく → よろしう → よろしゅう
- おおきい → おおきく → おおきう → おおきゅう
- う + う → うう
Examples:
- にくい → にくく → にくう
- やすい → やすく → やすう
- え + う → よう
I can't find any adjective examples involving the ～え → ～う shift, simply because there are so few adjectives ending in -ei (I can only find 執念【しゅうね】い, "stubborn, persistent"). However, there are other historical examples we can show:
- 今日 was けふ (//kepu//) in Old Japanese. That medial //p// lenited (softened) first into //f// producing //kefu// (technically //keɸu//), then into nothing, leaving けう (//keu//). That then shifted into modern きょう.
- 食べよう ("let's eat") was formerly たべむ. That medial //m// lenited, producing たべう. In roughly the Muromachi period, this was pronounced more like たびょう, until the volitional ending was re-analyzed as suffix ～よう, producing たべよう.
- お + う → おう
Examples:
- おおい → おおく → おおう
- すごい → すごく → すごう
Morphology and okurigana
Broadly speaking, okurigana are added onto the end of a kana spelling to indicate that portion of the reading that varies with different conjugations.
Sometimes this reflects changes that used to happen in Classical Japanese and earlier, but that don't happen anymore. Two whole classes of verbs reflect this: the so-called 上【かみ】一段【いちだん】活用【かつよう】動詞【どうし】 (literally "upper monograde conjugation verbs"; kami or "upper" refers to the い vowel that appears on the end of the verb stem, and い is considered "higher" than え, the end of the other kind of monograde verb stem), and the 下【かみ】一段【いちだん】活用【かつよう】動詞【どうし】 (literally "lower monograde conjugation verbs", where shimo or "lower" refers to the え vowel that appears on the end of the verb stem, and え is considered "lower" than い).
The ichidan or "monograde" part refers to the fact that there is only one verb stem for all of the conjugations. Let's look at two verbs as examples:
| Form |
Kami verbs with "i" stems |
Shimo verbs with "e" stems |
終止形【しゅうしけい】
Terminal / predicative
(dictionary form) |
[起]{●}[き]{●}る
okiru |
[食]{●}[べ]{●}る
taberu |
未然形【みぜんけい】
Incomplete / irrealis
(for negatives, etc.) |
[起]{●}[き]{●}～
oki- |
[食]{●}[べ]{●}～
tabe- |
連用形【れんようけい】
Continuative / infinitive
(for ～ます, etc.) |
[起]{●}[き]{●}～
oki- |
[食]{●}[べ]{●}～
tabe- |
連体形【れんたいけい】
Attributive
(for modifying nouns) |
[起]{●}[き]{●}る
okiru |
[食]{●}[べ]{●}る
taberu |
已然形【いぜんけい】
・仮定形【かていけい】
Realis / hypothetical
(for conditionals, etc.) |
[起]{●}[き]{●}れ～
okire- |
[食]{●}[べ]{●}れ～
tabere- |
命令形【めいれいけい】
Imperative
(for making commands) |
[起]{●}[き]{●}ろ・[起]{●}[き]{●}よ
okiro / okiyo |
[食]{●}[べ]{●}ろ・[食]{●}[べ]{●}よ
tabero / tabeyo |
As you can see above, the verb stem portion remains the same for all verb forms.
However, in Classical Japanese and older stages of the language, both of these conjugation paradigms used to be 二段【にだん】 or "bigrade", and that last kana on the verb stem used to also change. In these older conjugation paradigms, the nidan or "bigrade" part of the name refers to the alternation between either "i" and "u", or "e" and "u", as seen here:
| Form |
Kami verbs with "i" stems |
Shimo verbs with "e" stems |
終止形【しゅうしけい】
Terminal / predicative
(dictionary form) |
[起]{●}[く]{●}
oku |
[食]{●}[ぶ]{●}
tabu |
未然形【みぜんけい】
Incomplete / irrealis
(for negatives, etc.) |
[起]{●}[き]{●}～
oki- |
[食]{●}[べ]{●}～
tabe- |
連用形【れんようけい】
Continuative / infinitive
(for ～ます, etc.) |
[起]{●}[き]{●}～
oki- |
[食]{●}[べ]{●}～
tabe- |
連体形【れんたいけい】
Attributive
(for modifying nouns) |
[起]{●}[く]{●}る
okuru |
[食]{●}[ぶ]{●}る
taburu |
已然形【いぜんけい】
・仮定形【かていけい】
Realis / hypothetical
(for conditionals, etc.) |
[起]{●}[く]{●}れ～
okure- |
[食]{●}[ぶ]{●}れ～
tabure- |
命令形【めいれいけい】
Imperative
(for making commands) |
[起]{●}[き]{●}よ
okiyo |
[食]{●}[べ]{●}よ
tabeyo |
The changeability of that last kana in the stem is why the き and the べ are still included in the okurigana for these verbs -- even though that last kana of the verb stem no longer changes in modern usage.
Looking back at that ～とう ending
The treatment of okurigana for the ～とう ending has some parallels to the treatment of okurigana for ichidan verbs. Since the た portion of the ～たい ending doesn't functionally change into a different kana, that た is treated as part of the unchanging stem of the adjective.
Granted, the sound changes from ta to to. However, this only reflects euphony through the fusing of adjacent vowels. That's what I mean when I say that this isn't a functional change -- the sound shift does not indicate a change in conjugation forms.
Consequently, this ～とう ending is still treated as if it were ～た (part of the stem) + う (adverbial suffix) for purposes of figuring out the okurigana, and thus this ～とう is morphologically treated as two units instead of one.
