*NP if NP is phonetic and NP has no Case.
Yes; If NP is marked as [-Case_Inh], then the absolute value of Case must be determined. If it is not determined, the form will crash (be rendered ungrammatical).
See *john painted both those three house.a) Both is [+Daul] and three ios -Dual]; they do not agree.
house is [-Pl] and three is [+Pl]; they do not agree.
See *john painted both those three house.b) Much is [-Ct], students is [+Ct]; they do not agree.
the is [+Def], some is [-Def]; they do not agree.
(1c) Saw is marked [-Nom], him is marked [+Nom; they do not agree.
Note. What is important here is to get [Nom] from the verb to Ca to DP/NP. There are two ways to do it: via UqP/DP as indicated above are trough UQ. This was never brought up in class, so no marks off here as it gets to DP/NP via one of these methods.