Is it possible to have one Sql-Server cluster node in multiple Sql-Server clusters?
Is it possible to create FAILOVER CLUSTER A with Node01 (active) and
  Node02 (passive) and FAILOVER CLUSTER B with the same Node02 (passive)
  and Node03 (active)?


No you cannot. This is enforced by Windows Server Failover Clustering.


  I realized that SQL Server instances on passive nodes are not charged,
  only the OS. So sharing a node for more than one passive Sql-Instance
  would make sense here. I know, once cluster A and cluster B have an
  issue I am nipped...


There is nothing stopping you from creating a 3-node cluster (all nodes in the same cluster) and installing two SQL Server FCIs. You'll get roughly the same results.