Need Help With Database Design.

I guess I am confused about something and need some help. I am looking at a database schema for about 20 tables in a database. I noticed that the first
column in each table Is some type of Id. For example StudentId,TestId etc.
Where the Id is a unique numeric sequential value.

So I have some questions?
1- Do these Id's act as what are called indexes for the table?(Unique indexes)
2- If the answer to 1 is correct, then how do I create these unique indexes?
   Is it as simple as declaring the Id column as the primary key and that this
   value will be generated automatically upon insert?
3- Is it necessary to have an Id column for every table, or may I only do it
   for a few of them?
4. In relation to Question2, what do I need to do, so that the Id column will
   automatically be created when someone inserts a value into the database
   table with an ID column.


For example here are two sample tables

StudentsInfo

StudentId<PK>   Name   Age
1               Mark   33
2               Jill   23  
3               Mary   25

PersonalInfo

Name<FK>  SocialSecurity   Address    Major
Mark      324-444-3342      15 Elm    Art
Jill      888-888-8998      21 North  Science
Mary      876-777-2344      18 Byle   Music