SUMO provides four routing algorithms including Dijkstra. Does it uses variable Dijkstra to avoid congestion on new route? Means whenever a vehicle is rerouted, whole network is investigated again to find shortest / fastest path?
Yes, SUMO can do fully dynamic rerouting. The first link given in the comment by Julian Heinovski basically answers this. This is not necessarily a question of the routing algorithm but rather whether a rerouting device is used. So only when using the device you will get the fully dynamic behavior.