This is also what interests me. In fact I always hesitated to download a pdf file of the published articles and finally never did it. But I notice that some people do it. I know that while publishing an article in some Journals you are asked to pay and get this right. But I never asked for it because this is expensive. I do not know whether APS allows such downloads. Can anyone comments on the relevant legal rights.
One can use post print verson of publication excluding page no , journal name etc., If publisher specifically mention about copy right then link of paper can be given. I have seen many papers which authors put on their institutional website or personal webpage.
Yes, you can do it. Just look at the "Show self-archiving restrictions" section at the bottom of page in RG (just below the details of your paper). You can find the journal policies regarding the paper and if it is allowed to share it on RG or not. There are three options - red, green and yellow. If it is 'green', you can publish it here. Also many journals which are open access have no restrictions when you use your own paper in an online repository like RG. Depends on the journal policies. If they permit, you can. In most of the cases, there is no restriction. Some restrict for 12 months after the publication date. But it is better to check it as the facility is available through research gate itself.
One should be quite careful with the copyright and for this very reason almost always it is not OK to post the PDF from the publisher. For instance, Elsevier has recently asked the authors to remove the PDFs of their papers on academia.edu: