Should I put mortar under my stepping stones?

not under, unless they are over a concrete surface to begin with -- if on sand base, just pack the gravel/sand between the stones and be sure the sub surface is well packed -- you can rent 'packers' from rental tool places --

You can. It will help contain the gravel and weeds. Most just use sand that is tamped down.

NO! Lay down some landscape fabric for drainage and weed prevention first. Then lay out your stepping stones. Gravel goes next surrounding the stones.

First dig down the walkway 3" then put down landscape fabric, then gravel, tamp down, add sand tamp down, then add your stones, and use a level to work them with sand to level. Then add a layer of polymer sand to hold in place and use a broom to smooth.

I agree with William, not the best idea- good luck:)