Can the distributor be contaminated by the coolant from the flush service?

If they were not careful and let the coolant spray around while they were doing the flush it can go pretty much anywhere. If it sprayed onto the distributer cap it would coat it with a thin layer that is conductive. It could also get into the connectors if they are not sealed very well, which most are not that good. It is the same reason that people are warned not to wash the engine off in a car wash. The spray can get into places you don't want it to go and do damage.

Yes it could, that would be one reason for the stop leak. With it forcing out coolant and air it is a likely reason they tried it as well. I would run the tests listed in the guide below and see what you have. If it is a head gasket, as it sounds like, you may want to do a full coolant system flush, and a heater core flush then decide how to deal with the head gasket issue. Leaving the stop leak in there could block up the heater core and cause more problems. It could also be that something has a crack like the head or block, both can push combustion gas into the cooling system. For that using the pressure test may show it better.

https://www.2carpros.com/articles/head-gasket-blown-test