Disubstituted cyclic alcohols - looking for IUPAC rule
For preferred IUPAC names, the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), explicitly stipulates when locants are omitted. Most of these rules apply to the omission of the locant ‘1’.

In particular:


  P-14.3.4.2 The locant ‘1’ is omitted:
  
  (…)
  
  (c) in monosubstituted homogeneous monocyclic rings;
  
  (…)


One example for this rule given in the Blue Book is cyclohexanethiol. Likewise, cyclopentanol is the preferred IUPAC name for the first compound that is given in the question.



This rule, however, is not applicable to the other two compounds that are given in the question since they are not monosubstituted.

Furthermore, we can find a general rule that is relevant in this case:


  P-14.3.3 Citation of locants
  
  In preferred IUPAC names, if any locants are essential for defining the structure of the parent structure or of a unit of structure as defined by its appropriate enclosing marks, then all locants must be cited for the parent structure or that structural unit. For example, the omission of the locant ‘1’ in 2-chloroethanol, while permissible in general usage, is not allowed in preferred IUPAC names, thus the name 2-chloroethan-1-ol is the PIN. (…)


Therefore, the preferred IUPAC names are cyclopentane-1,1-diol and 1-methylcyclopentan-1-ol, respectively. The omission of the locant ‘1’ is not permissible for the preferred IUPAC name.





Nevertheless, the name ‘1-methylcyclopentanol’ describes the correct compound and may be used in general nomenclature.