Recommendation on changing Azure SQL Database tier weekly
Azure SQL Database is designed to scale up and down based on your workload. I cannot answer your question "is it ok to change the tier to S0 every weekend for cost savings and change back to s6 on Monday" with yes or no.

You also mentioned usage is very minimal. S0 gives you maximum 10 DTU. Do you know for your "very minimal" workload 10 DTU is enough or no. Is your application written to retry disconnected sessions?

From books online:


  Existing connections to the database in the original compute instance
  are dropped. Any new connections are established to the database in
  the new compute instance. For some combinations of service tier and
  compute size changes, database files are detached and reattached
  during the switch. Regardless, the switch can result in a brief
  service interruption when the database is unavailable generally for
  less than 30 seconds and often for only a few seconds. If there are
  long running transactions running when connections are dropped, the
  duration of this step may take longer in order to recover aborted
  transactions. Accelerated Database Recovery can reduce the impact from
  aborting long running transactions.


Few other resources for your third point "any other steps to perform prior tier change and suggestions please".


Scale single database resources in Azure SQL Database
Recovering from a possibly failed scale-up
Stop / Cancel ongoing Azure SQL DB scale operation
sys.dm_operation_status (Azure SQL Database)