If the design patent constitutes prior art that would render your utility patent invalid on grounds of anticipation (lacking novelty) or obviousness, then it could prevent you from achieving a patent, This is true even if the design has a functional utility. In fact, if the design patent has been available to the public for more than a year and if the utilitarian functions are inherent in the design, the design patent would most certainly invalidate your patent because it would inherently disclose your invention even if the invention was not claimed. The owner of the design patent had no obligation to obtain a utility patent---and if the product that is covered by the design patent also has a utilitarian function, that design patent (and the product described which is also in the prior art) can prevent you from obtaining a patent on grounds of anticipation/novelty.
I think that it will depend on whether by looking at the design, a person skilled in the art would also understand a functional utility purpose. If the utility purpose is not apparent from the design, then that design patent would probably not stop you from getting a utility patent.
Design patents can be used as prior art against utility patents. There is no law or US PTO rule that prohibits a design patent from being used as prior art against a utility application. A design patent does not claim functionality, but that does not mean that functionality is not inherently disclosed or obvious in light of the design patent.
Disclaimer: This answer does not constitute legal advice and does not create an attorney-client relationship.
Yes. Design patents are frequently cited against patent claims in a utility patent. If the design patent is either identical to the claimed invention or makes the claimed invention obvious to a PHOSITRA (person having ordinary skill in the relevant art) the claimed invention is unpatentable under 35 USC 102/103. You might have a valid claim to an unknown and non-obvious use for the item in the design patent, but not to the shape or appearance disclosed in the design patent. You are struggling with basics of patent law and that tells me you for sure need to see a patent attorney so you can find out the answer for your specific situation.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.