WRT the second part of the question (which makes the question a bit incoherent), a number of languages also contrast the phonatory properties of glottalization and breathiness for vowels. In Badaga, retroflexion is contrastive. Rounding is considered to be a "place of articulation" property, so since you mention rounding separate from POA, I would suppose you have a different conception of POA, in which case you may want to know of "pharyngeal constriction" which is a feature of some dialects of Aramaic and Interior Salishan languages, and possibly Berber dialects -- however, sometimes the locus of the distinction is said to be a consonant (as in Arabic). "Advanced Tongue Root" is another distinctively vowel feature. "Pharyngeal constriction" is not ever contrastive with ATR, and since ATR (and pharyngeal constriction) are not particularly coherent from the perspective of crosslinguistic phonetics, they could be subsumed under one category, with difference in physical details being phonetic implementation. Some Khoisan languages have "epiglottalization" as a feature.
Voicelessness contrasts in Comanche vowels (see J. Armagosts's paper), for example [u kúʔokʷekʷai uʔ] "she went to render it" vs. [u kúʔokʷe̥kʷai uʔ] "she rendered it and went on". A's discussion is classic, in underscoring how fruitless questions about "phonemic" status are unless you define and defend your terms. The surface form [tókʷi̥te] "peep" comes from /to-wihte/, and surface voiceless vowels can be derived by rule, in this case affecting unaccented vowels before coda /h/ (as well as /s/). The reason why voicelessness is phonemic in the surface-oriented perspective is that the thing that conditions devoicing, h, is itself deleted, so if you can only appeal to things present in the surface form for determining the phonemic status of a segment, then voicelessness is phonemic, yet fully predictable.
There is direct evidence from alternations, e.g. the related form [wíhte] "peep", which shows in this instance that the /Vh/ analysis is correct. There may be no such evidence in [náki̥nɨɨ] "ears", so while we know that in "peep" that the voiceless vowel must be derived from a voiced vowel, we can't say that that same analysis is mandatory in numerous cases. However, forms like [náki̥nɨɨ] clearly do not require underlying voicelessness on vowels.
Your question can then reasonably be interpreted in two ways. One is from the strictly surface-oriented perspective, and the answer is that yes, a number of languages have voiceless vowels. The other is from the perspective of a theory that there are no underlying voiceless vowels, and you are asking about counterexamples to that conjecture. Comanche is not a strong counterexample, since (apparently) voicelessness can be eliminated in favor of a vowel-h cluster analysis. And as far as I know, such a reanalysis is always possible for putative underlying voiceless vowels.