How do you update multiple field using Update.Set in MongoDB using official c# driver?

It's very simple ;), just add another set or some else operation to the your update:

 var update = Update.Set("Email", "[email protected]")
                    .Set("Phone", "4455512");

You can also use the generic and type-safe Update<TDocument>:

var update = Update<Person>.
    Set(p => p.Email, "[email protected]").
    Set(p => p.Phone, "4455512");

For conditional updating you can use something like

        var updList = new List<UpdateDefinition<MongoLogEntry>>();
        var collection = db.GetCollection<MongoLogEntry>(HistoryLogCollectionName);

        var upd = Builders<MongoLogEntry>.Update.Set(r => r.Status, status)
            .Set(r => r.DateModified, DateTime.Now);
        updList.Add(upd);

        if (errorDescription != null)
            updList.Add(Builders<MongoLogEntry>.Update.Set(r => r.ErrorDescription, errorDescription));

        var finalUpd = Builders<MongoLogEntry>.Update.Combine(updList);

        collection.UpdateOne(r => r.CadNum == cadNum, finalUpd, new UpdateOptions { IsUpsert = true });

Or just pop out the record, then modify and replace it.