Question about Privileges

Assume that I have the following database:

Database:    mydb
Schema:      mydb_schema
Tables:        mydb_table1
                   mydb_table2
                   mydb_table3   

I create a role:     Create Role dbuser LOGIN;

mydb=# grant all privileges on mydb_schema.mydb_table1 to dbuser;
mydb=# grant all privileges on SCHEMA mydb_schema to dbuser;

Remotely connect dbuser to mydb and run SELECT:
mydb=#select * from mydb_schema.mydb_table1;

Here I want to do a SELECT on mydb_table1 as the above line shows. It seems to me that I have to grant Privileges to dbuser on both the  mydb_schema and mydb_table1 so that the dbuser can run SELECT.
If there are 10 tables under mydb_schema, do I need to grant privileges to the dbuser  on all the 10 tables individully so that dbuser can operate the 10 tables?

I also find that if I only grant privileges on database to dbuser as below, without granting privileges on Schema and table to dbuser, dbuser still can not do SELECT on the tables.
mydb=# grant all privileges on Database mydb to dbuser;

Is there any simple way to grant All privileges to dbuser on all the 10 tables?

Thanks.

Jack