I agree with Bevan. Here are some answers specific to your questions:
(I'll make the assumption you're talking about Oracle)
Can I see the other functions that are
in sys?
Yes, like any schema you can view the procedures, functions and packages in sys using a database development tool such as Toad, PLSQL Developer or Oracle SQL Developer. However my experience has shown that referring to Oracle documentation (freely available online) is a better way to learn about the available functionality than jumping straight to the source code.
What is the query for doing so?
I'd recommend the use of one of the development tools above. Failing that, try:
select * from user_objects where type in ('PACKAGE', 'PROCEDURE', 'FUNCTION');
Once you've found the functionality you're looking for use the DESCRIBE command in SQLPlus to determine the method signatures and data types.
In what situations is this sys useful?
SYS is most often often used as a super user for adminstrative tasks as it has more privileges than a common schema. SYS also contains a lot of the infrastructure on which Oracle depends - don't mess around with the objects that SYS owns.
Where will be the information about sys is stored in database?
Use the methods I have suggested above - but I recommend you read the online documentation rather than dive straight into the source.