For verbs with irregular humble/honorific forms, are the regular forms still used?

Question

• There are verbs with irregular humble forms, e.g. the humble form of 借りる is 拝借する.

  For these verbs, are the "normal humble conjugations" still used, or considered grammatical?
  Would お借りする be acceptable?

• Similarly, there are verbs with irregular honorific forms, e.g. the honorific form of 食べる is 召し上がる.

  For these verbs, are the "normal honorific conjugations" still used, or considered grammatical?
  Would お食べになる and お食べです be acceptable?

Answer 1

“Are they used?” and “Are they acceptable?” are different questions. The regular forms such as お借りします and お食べになります are used, but they are less formal than the irregular forms such as 拝借します and 召し上がります. Whether the less formal expressions are acceptable or not depends on how formally you want to speak.

By the way, you are confusing grammatical terms “respectful form,” “humble form,” “polite form,” and “honorific form.” 拝借します is the polite form of the humble form of 借りる, where the humble form of 借りる is 拝借する. 召し上がります is the polite form of the respectful form of 食べる, where the respectful form of 食べる is 召し上がる. Whether an expression is in polite form or not is orthogonal to whether it is in respectful or humble form. Honorifics are the broader concept which includes all of respectful form, humble form, and polite form. For details, see Wikipedia.

Answer 2

For some of the verbs with irregular respectful and/or humble forms, the corresponding regular forms are also used, e.g. お借りする, お食べになる, although they usually sound less formal.

For some, most of which compose of two moras, that's not the case, e.g.:

行く　?お行きになる|いらっしゃる　*お行きする|参る

来る　*お来になる|いらっしゃる　*お来する|参る

見る　*お見になる|ご覧になる　*お見する|拝見する

言う　?お言いになる|おっしゃる　*お言いする|申す

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