SQL Cluster 2005, windows 2003 urgent

hi all,

we have installed sql server 2005 cluster on the active node with virtual name sqlcluster and the instance name to be sql 01, it automaticallysql server on the other node(the passive node).
however it did not install the management studio on the other nodeand we failed over from primary to secondary and installed the management studio.

but on the primary node also, the same instance name exists.

system databases were put on the shared array instead of local C drives, is that normal.

if we have a sql serve sluster dont we have two seperate sql server instance names and one virtual cluster name.

pls help.thanks  a lot in advance