#[Japt](https://github.com/ETHproductions/japt), <s>61</s> <s>59</s> <s>92</s> <s>85</s> 84 bytes

> I'm offline for most of the (long) weekend, if any more issues are discovered with this, please ask a mod to delete it for me until such a time as I can fix it.

Takes input as a string for both operations and returns a string for both as well or `false` for invalid input.Assumes number inputs will always contain multiple digits, add 1 byte replacing `UÉ` with `Un<space>` if that's not valid. Returns `false` for test case `GIGATESTER` but, according to the rules, that *should be* invalid input.

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    V="OIREASGTBP"UÉ?¡VgXÃe"%v"²_i1'NÃe"%V"²_i1'UÃ:!Uè"%v%v|%V%V|[^{V}NU]" ©Ur"N|U" £VaX

**Try it:** [Numbers -> Letters](http://ethproductions.github.io/japt/?v=1.4.5&code=Vj0iT0lSRUFTR1RCUCJVyT+hVmdYw2UiJXYisl9pMSdOw2UiJVYisl9pMSdVwzohVegiJXYldnwlViVWfFtee1Z9TlVdIiCpVXIiTnxVIiCjVmFY&input=IjMxNDE1OTIiCg==) or [Letters -> Numbers](http://ethproductions.github.io/japt/?v=1.4.5&code=Vj0iT0lSRUFTR1RCUCJVyT+hVmdYw2UiJXYisl9pMSdOw2UiJVYisl9pMSdVwzohVegiJXYldnwlViVWfFtee1Z9TlVdIiCpVXIiTnxVIiCjVmFY&input=IkVOSU5BTklTVVBVUiIK)

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- <s>2</s> 4 bytes saved thank to [obarakon](https://codegolf.stackexchange.com/users/61613/obarakon), who also convinced me to take this up again after I abandoned it earlier. I wish he hadn't!
- <s>33</s> <s>26</s> 25(!) bytes sacrificed implementing a quick fix (i.e., yet to be fully golfed) to check input validity.

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##Explanation
(Yet to be updated to the latest version)

                              :Implicit input of string U.
    V="..."                   :Assign the string of letters to variable V, in order.
    UÉ                        :Subtract 1 from U, which will give a number (truthy) if the input is a number or NaN (falsey) if the input is a string.
    ?                         :If it's a number then
    ¡                         :    Map over the input string, replacing each character (digit) with ...
    VgX                       :      the character in string V at index X, the current digit.
    Ã                         :    End mapping.
    e                         :    Recursively replace ...
    "%v"²                     :      every occurrence of 2 vowels (RegEx) ...
    _i1'N                     :      with the current match with an "N" inserted at index 1.
    Ã                         :    End replacement.
    e                         :    Another recursive replacement of ...
    "%V"²                     :      every occurrence of 2 non-vowel characters (i.e., consonants) ...
    _i1'U                     :      with the current match with a "U" inserted at index 1.
    Ã                         :    End replacement.
    :                         :Else, if it's a string then
    Uè"%v%v|%V%V|[^{V}NU]"    :    Count the number of matches of 2 successive vowels OR 2 successive non-vowels OR any character not in contained in string V plus N & U.
                              :    (The longest part of this code is the fecking input validation!)
    ?                         :    If that count is greater than 0 then
    T                         :       Return 0.
    :                              Else
    Ur"N|U"                   :        Replace every occurrence of "N" OR "U" in string U with nothing.
    £                         :        Map over the string, replacing each character (letter) with ...
    VaX                       :         the index of the current character X in string V.
                              :Implicit output of resulting string