On the Q's off 2 items or 3 items, you should be able to use the free one as an item. It shouldn't matter who pays for it as long as it runs through the register as an item.
On the BOGO Q, that is very YMMV depending on your RiteAid. We had this discussion for the Loreal Vive Pro in the past couple weeks. All the registers from different stores don't ring the items up the same. Some ring the first one at full price & the second free (as you would expect with BOGO) while others ring each item at 1/2 price.
My store rings them at 1/2 price so the BOGO Q with BOGO sale still leaves me oweing 1/4 the price for 2 items (i.e. - Item retail $4.99, each rings $2.49 for their free portion - Q takes $2.49 leaving me to pay $2.49/2). Others who had stores where it rang normally did the deal fine.
I don't fool with BOGO Q's at RiteAid anymore because of how my local store does. You won't know for sure until you try. If they don't give you the deal you want, leave them the stuff & keep your BOGO's for use elsewhere......