Understanding of SQL Server active/active cluster I have a vague understanding of SQL Server's active/active cluster. Can anyone help to confirm if my understanding is correct?

As I understand, active/active cluster use two or more Windows servers. Let's say we have two servers n1 and n2. Then we create a failover cluster on those two servers and join n1 and n2 into the cluster. Then we install a SQL Server instance i1 on n1 and n2. After that we install another SQL Server instance i2 on n1 and n2. Then we can start i1 on n1 and start i2 on n2 to make a active/active cluster. Later we can failover i1 from n1 to n2 and failover i2 from n2 to n1. 

Is my understanding correct? Do we need to install the instances i1 &amp; i2 on both n1 and n2? After the installation and configuration of the active/active cluster, how many SQL Server services are installed and running on each node?
You've essentially got it right.  Active/Active is really just a multi-instance SQL cluster.  When you install the Failover Cluster Instance (FCI) I1 on N1 of the Windows Server Failover Cluster (WSFC) you then have to run Add Node on N2 of the WSFC for I1, and vice versa for Instance I2. The SQL Server and Agent services are installed on both nodes, but will only be actively running on the node that actively has control of the SQL Instance.