signature on the back of the canvas

I think that it is good to apply writing to the stretcher bars but I realize that sometimes these may become separated from the painting in the future. There are four main considerations when deciding to write on the back of a canvas. First, make sure that the media does not require you to press hard when writing on the reverse, especially on grounds/paint that may have become brittle overtime. I have seen paintings where the writing on the back has physically telegraphed through to the painted surface as a very fine raised crack which could be read when looking at the face of the painting in raking light. Second, the writing should be thin in consistency and not drastically change the texture and topography of the bare canvas. Anything substantive applied to the back of a canvas like thicker paint, labels, and patches usually come forward do to the alignment of physical forces and will cause the front of the canvas to protrude in a noticeably manner. Third, the media used should not harm or drastically stain the fabric. This would really rule out dilute oil paint which would cause the drying oil to bleed into the surrounding canvas. Finally, you would want the writing media to be coherent and adherent enough so that it does not simply fall away over time like charcoal or possible fade due to the use of fugitive dyes, like some markers. So given all of the above. I would suggest using diluted India ink of something like a carbon black pigmented technical pen (or pen/brush) or the disposable alternatives available today and be gentle when writing on the back. It would probably help to have the painting face down on a soft sheet of blotter when you do this to avoid pressing too hard. Dilute acrylic dispersion paint applied in a rather dry manner (trying to not get the back too wet) should work fine as well. Darker, and slightly softer, graphite pencils gingerly applied are a fine alternative as well. There are probably other options but those are what come to mind.

I would not suggest applying a fixative to the back of a canvas. This will create regions that respond differently to changes in relative humidity. Probably a very light application may not cause problems but its efficacy at fixing the charcoal would be proportional to the degree that it changes the surface of the canvas and the degree to which it may eventually cause planar deformations.