Is it possible to configure only one secondary and one primary in MongoDB Replication?
Yes! Of course!
But in the situation where you lose one of the nodes (primary or secondary), remaining node state will be secondary and you cannot insert/update/delete data. If you can add (one) arbiter to that replica set, your DB will keep working even you lose one node. Basically arbiter don't need many resources, smallest VPS node what you can find is enough. (512MB memory, 1 CPU, 10GB diskspace) OR you can even add that arbiter to that application machine what is connecting to that mongoDB.