ある年のこと、大雨が切れめなく、ザアザアふったので、村は水びたしになってしまい、村人は、 とてもこまりました。
I don't understand the second part "村は水びたしになってしまい". I figured out that this means "The village ended up becoming dipped in water." But some transformations I don't get. For example, how and why the verb ひたす became びたし, which form I didn't manage to find in the internet at all. Also subsidiary verb しまう(which follows the TE-form of なる, and adds the nuance of "end up", "unfortunately") somehow became しまい.
how and why the verb ひたす became びたし
The ひ → び sound change is [連濁]{れんだく}.
みず + ひたし → みずびたし (水浸し)
あさ + かお → あさがお (朝顔)
ひら + かな → ひらがな (平仮名)
さん + ひき → さんびき (３匹)
For more on 連濁, see:
びたし (or ひたし) is the noun form of the verb [浸]{ひた}す. It's originally the continuative form (連用形) of the verb. For more on the noun form of verbs, see:
The subsidiary verb しまう [...] somehow became しまい.
The しまい is the continuative form (連用形) of しまう. This form can be used as a conjunction. 「水浸しになってしまって、村人はこまりました。」 means the same thing as 「水浸しになってしまい、村人はこまりました。」 The latter sounds a bit more literary.
This form is called [中止形]{ちゅうしけい} and this usage, [中止法]{ちゅうしほう}. See:
