Yes, you can have more than one database on the same server. However, if you are going to just be testing a few statements, it might be easier to clone the tables and use the same database (this may or may not be frowned upon by your employer - check first!). Create a test schema and copy the tables into the test schema. In order to avoid any possibility of honking up your production data, give the tables similar but different names. Also, you might want to limit the data to a subset of the real data - not only will this speed up your test queries and take up less storage, but it will also make it easier to tell if you have a cartesian join. To clone the table, try the following:
CREATE TABLE test_schema.test_my_table AS
SELECT * FROM production_schema.my_table
WHERE rownum < 11; <= This will give you ten rows of data.
Note that this will copy the structure and data, but not indexes, constraints, or triggers. This may be a problem, depending on what you are working on - just getting the SQL right or tuning for performance.
If this approach works for you, it's a LOT easier than cloning an entire database.