If you want to extend the profile properties, you can just use "Add Property" from the Admin -> Users -> Manage Profile.

I don't really see what that has to do with identifying the user, though.  It's easy to identify a specific user simply using UserID; that's always unique.

As for a solution to the scenario, it really depends on what you mean by "information will then be uploaded".  Are you talking about a file, multiple files, database data, etc?  It would be a pretty simple module to just have an Edit form that allowed you to input data and/or upload documents.  If one of these fields was something like "Access for user:" and you selected the authorized user, then you could write your View page in a way that when a logged in user access your module, they see the information you input/uploaded.  Is that what you're talking about?

Ok, still pretty easy.  Per usual, there are multiple ways to skin this cat.  First, the easy answer, 

"How can I access the two custom fields for a user in code to retrieve only user specific information?"

To extract / set custom profile information, you can use:

UserInfo.Profile.GetPropertyValue(Name)

and

UserInfo.Profile.SetPropertyValue(Name, Value)

Now all you have to do is write your modules.  You can do this with one module that has two definitions: one to enter details for a parking infraction and a second for user to view/pay? their infractions and fine.  Doing it this way you are really going to end up with two view modules.  The benefit is it will be easier to access data to/from each of them because it's all in the same class.  This should be pretty straight forward. 

What I would do is write the infraction entry page first.  This is pretty much a simple form that includes Vehicle Registration and/or National Identity Number.  Once you have your parking infractions table, all you need is a view page for users to find theirs.  This module needs some logic to retreive the current logged in user's extra profile fields.  Maybe something like:

VehReg = UserInfo.Profile.GetPropertyValue("VehReg")
NatID = UserInfo.Profile.GetPropertyValue("NatID")

Then you just query the table you stored the infraction data in and look for a match on either of these two values.