What is the ruling on congregational prayer in a resting place instead of the mosque upon hearing the call, and is the call via loudspeaker from a distant mosque considered a basis for obligatory congregational prayer, or is what matters the estimation of the call without a loudspeaker?

There is no objection to praying in the resting place — especially if going to the place of the call is difficult — and by doing so, the virtue of congregational prayer is attained, because going to the mosque is not obligatory except for those who are not already in a congregation. Prayer areas do not have the same ruling as mosques. The call that necessitates going to attain the virtue of congregational prayer is the regular adhan (definition) that can be heard without a loudspeaker.