Usually, when conjugating Godan verbs ending with う into て-form, you would get って instead. Is there an etymological reason for this exception for 乞うて? I saw this in a rather recent book written in the last ten years, so would the modern Japanese progressive form of 乞う be 乞うている?

I've also read that some other verbs also use this conjugation, but it sounds rather archaic. For example, 問う→問うて、沿う→沿うて. Are there other verbs that conjugate this way in modern Japanese?