I have a document  residing in a document library  in a site under Sites
Directory. I selected a document and chose "Submit to Portal Area".
Under the location area, I selected document library. How come when I
navigate to the main portal and under document library I do not see the
document I just submitted?

When you choose to "Submit a document  to Portal" you are actually
creating a listing to that document, not a copy of the document in the
portal. Therefore, the document stays where it is and you should see a
listing at all locations you submit the document to. You have to have
the Grouped Listings web part showing to see the listing.

Regarding your other question about the different "Links" web parts, I
really don't understand all of these either. I tend to use the My Links
to add links to my personal portal site and just the Links web part to
display links on public portal sites. I'd guess the Links For You part
has something to do with audiences, but I really don't know.

I assign users to have access to their own site
under Sites Directory. If a user from a site wants people outside his
site to view the document, he submits the document  to a portal area,
doesn't the other users need to have reader rights to the site in order
to view the document from the portal area under Group Listing? If this
is the case, then it grants those users reader right to access that site
and this is not what we want. How do we just grant the users access to
the documents  without granting them access to the site? Is this where
audience come into play?

You have a couple of options here that I can think of:

1. Instead of granting users personal sites in the sites directory,
encourage them to setup a MySite area and put documents  in the Shared
Documents folder. They can then create listings to those documents
without comprising more private items.
2. To get more granular security on a document, consider having the
users create workspaces specifically for those documents. This feature
is one of the selections from the drop down list of DM features in the
doc library.

For #1, I came in as two different users (UserA & UserB). UserA uploaded
a document  into the Shared Documents. It shows up under Group Listings,
Document Library, News and Links for you web parts for UserA & UserB.
But when I go in as UserA and delete the document, those web parts still
displays the link to the document. Why? And then weird thing is when I
go in as UserB and try to upload a document into the Shared Documents,
none of the web parts display that new document.

For #2 below, I created a document workspace under one of the site. But
users outside of that site cannot access that document workspace. It
only recognizes users within that workspace.

This document library  stuff is too confusing.

Let me rephrase the first paragraph below:

For #1, I came in as two users (UserA & UserB). UserA uploaded a
document into the Shared Documents, how do the other users see this
document because currently UserB cannot see this document. Also, all
documents that are added  to the document  library web part shows up under
Group Listings, Document Library, News and Links for you web parts. If
the document is deleted, how do you delete the link from these web
parts?

Please take a look at Tzunami Software.... It replaces the built in document
handling capabilities of Sharepoint, and replaces it with a much more
powerful document  management tool. It will automatically create meta data
and summary info when a doc is checked in. It will then automatically
create a taxonomy, or hierarchy, of documents  so users can locate
information my drilling through categories, rather then just receiving a
google style result set.

It is very easy to install and will drastically reduce administrative costs
and time. There is currently a 60 day trial... it works with v.1, but there
is a v.2 version set to be released in Sept...

i Need tzunami package and migration steps. I am trying to
migarate a sps2003 from one sever to another server.

How to move documents  from one document  Library to another Document
Library

There are a variety of ways - are you looking for something for an end user or a
programmatic approach?

Use explorer view in the document  library to move files in one shot...quite easy