Pam, you may want to substitute your tupenoid with Gamsol odorless mineral spirits, the best turpentine substitute I've found (so far). It's really odorless and mixes and cleans well.
About the linseed oil question, you can use it as a medium in most stages of the painting (not much sense in using it when you draw, or lay in the initial thin layers, for which turpentine is fine). I suggest you mix 2 parts linseed oil 1 part stand oil and three parts of Gamsol for an all - purpose medium, which you can use throughout the painting, even in the first stages. For the finishing layers, if you decide to try a special medium, there are a large number available, a good one is Grumbacher Painting Medium II. Specialty mediums, particularly the thicker ones, give you more control and 'feel' as well as transparency in any subtle layering and glazing. Alchemist brand mediums are outstanding, and can be ordered on the internet at
www.amberalchemist.com