Obviously, with a proper attribution. Thank you.
Normally yes, as long as you clearly cite the source (even if the license does not require it, plagiarism rules do) and of course the image should be appropriate for the research proposal (regardless of source). To be sure, carefully check any rules applying to your particular research proposal; it is possible (but unlikely) they have unusual rules that may prohibit this. For details on how to cite, see this summary page on Wikimedia Commons (thanks Buffy for the pointer). Note: most images on Wikimedia Commons are not public domain, but under another free license — check the specific image for details (it's even possible images have been wrongly uploaded to Wikimedia Commons, but there are limits in how far you can practically go to verify that the license information there is correct).