Would u use what ever u have whether is cotton or not (polyester for example ) as the backing ( face 2) of a quilt and why??

No. The fabrics wear different.

I have, in the past, used a poly cotton sheet, if I couldn't find a cotton one, but they were mostly small quilts. I have also backed several lap quilts with fleece for warmth.

Yes, main r small about 18" square or so

I have a couple of quilts that I did using many of the fabrics left from my grandmother's sewing scraps. There was double knit, poly, satin, tafeta, cotton... and probably anything else she would have used. They turned out great and wash very well. I've had no trouble with any of them

although i am very picky about the backs of my quilts i have used many different backing materials---some minkee---some fleece- some flannel- even corduroy- microfiber suede-
i choose the backing to go with the quilt--although i do not tend to use regular polyester fabrics- if that was what was going to work i would-
my only concern is making sure all can be cared for together- and who it is going to - how it will be cared for-
and i've made a few polyester quilts- for picnic/beach quilts- for the kids to make forts- go everywhere quilts-
i just make sure the fabrics in a quilt can all be cared for together- everything has to be wash/dry(able)
i have wool/silk quilts that are wonderful- with doublesided thick great flannel on the back-
i have quilts with silks, satins, cottons...

when deciding what to use in a quilt first think about who it is for/how it will be used and cared for- then choose your materials to work for that use/care---polyester holds up very well to frequent washings, wears like steel, does not shrink or fade---and pretty much stays the same as it is for it's life---(as in it does not soften up like cottons do)

i have used different types of fabric on the back. i don't expect most of my quilts to last for generations, so whatever works at the time will last as long as it will last.