The most important aspect here is clarity, and your first option is best for that.
I recommend against treating declined words out of context as indeclinable (casus generalis), unless you mark them with quotes of some kind.
With pronouns and other common words the reader might not parse them the way you intend.
Reading qui and quem in your second example sentence as declined pronouns makes the sentence a mess.
Quotes around the inflected word (or any other phrase for that matter) make the indeclinable status clear.
To clarify the syntactical role of the indeclinable, I would add a suitable noun in front of it.
That is, write Debes voce "qui" uti or In locutione "…" accusativo utimur.
If the case of the auxiliary word would be nominative or accusative or it would come with a preposition, leaving it out does not confuse too much.
In other situation the risk of confusion is significant.
I have been taught to use vox for "word" and verbum only for "verb", but I do not always do so.
Unless you need to discuss pronunciation, it might be better to reserve verbum for verbs and use vox or vocabulum for words in general.
Suggested translations of your examples:
- What is the possessive case of she?
Qualis est casus genetivus vocis "ea"?
- Should I use who or whom after man?
Debeone adhibere vocem "qui" aut "quem" post vocem "vir"?
Utro uti debeo post vocem "vir": "qui" aut "quem"?
- What is the past participle of run?
Quale est participium praeteritum verbi "currere"?