Generally, no, you don’t touch the area after moxibustion as part of what happens with moxibustion is the oils from the smoke entering the body through the open pores - so any other manipulation, creams, etc. is likely to disturb that.
As far as empty/full there would be no hard and fast rules there. While generally, you would tonify (i.e. use moxa) on an empty point - there are also many situations where dispersing an excess point would be called for - possibly to even out imbalances between sides. If you are unsure, it is likely best to stay towards the empty side, then watch the patient from treatment to treatment before considering dispersing.