Is it obligatory to perform ghusl after touching a dog before prayer? Are prayers performed before ghusl valid? And how should clothes that have touched a dog be washed if dust is not available?

The dog is ritually impure with a severe impurity (najasah mughalladhah). The impurity does not transfer merely by playing with it, unless its saliva, sweat, blood, or excrement touches a person, or if one touches it with wetness present on either or both (the dog or the person). However, if one touches it while dry, the impurity does not transfer. If the contamination with impurity is not known, the default is purity. If dog impurity afflicts (a place/person), the affected spot must be purified. The fatwa issued is the obligation to wash it seven times, one of which is with earth (or soap as a substitute). Some scholars hold the view that washing seven times is specific to containers, and that non-containers are purified by washing without specifying a number. If you were afflicted by dog impurity and did not wash it with earth, there is no obligation to make up the prayer according to those who do not see the obligation of washing seven times nor with earth. And whoever prayed with impurity due to forgetfulness or ignorance is not required to repeat the prayer. If the missed prayers were before puberty, there is no issue. However, if they were after puberty, then what was missed must be made up along with repentance.