Consistency levels are of two types, write consistency and read consistency. Consistency levels can be one, two, three or quorum. If it's quorum, atleast half of the nodes should be available for the operation. Otherwise (for one, two, three), the name itself gives you the definition.
Replication factor is the number of copies that you are planning to maintain in the cluster. If the strategy is simple, you will have just one replication factor. If you are having network topology strategy and is using multi dc cluster, then you have to set replication factor for each data centre.
In your scenario, if you have RF as 2 and CL as 3, it will work(I am assuming there are more than 3 nodes in the cluster and atleast one seed node). In this scenario, it will check whether three nodes are up and normal to receive the data and if the CL is met, it will write two copies to two nodes.
For your second question
When consistency level is set to 3, it means the results will be
acknowledged to the client after writing to the 3 nodes. If data is written to 3 nodes, then it gives me a replication factor of 3 and not 2..?
As far as I understood cassandra, It will not be acknowledged to cassandra. It just needs the CL to be met and the number of nodes acknowledged about new data will be equal to the RF.
So, there is no question in sacrificing RF.