how to log in to mysql and query the database from linux terminal

To your first question:

mysql -u root -p

or

mysqladmin -u root -p "your_command"

depending on what you want to do. The password will be asked of you once you hit enter! I'm guessing you really want to use mysql and not mysqladmin.

For restarting or stopping the MySQL-server on linux, it depends on your installation, but in the common debian derivatives this will work for starting, stopping and restarting the service:

sudo /etc/init.d/mysql start
sudo /etc/init.d/mysql stop
sudo /etc/init.d/mysql restart
sudo /etc/init.d/mysql status

In some newer distros this might work as well if MySQL is set up as a deamon/service.

sudo service mysql start
sudo service mysql stop
sudo service mysql restart
sudo service mysql status

But the question is really impossible to answer without knowing your particular setup.

1.- How do I get mysql prompt in linux terminal?

mysql -u root -p

At the Enter password: prompt, well, enter root's password :)

You can find further reference by typing mysql --help or at the online manual.

2. How I stop the mysql server from linux terminal?

It depends. Red Hat based distros have the service command:

service mysqld stop

Other distros require to call the init script directly:

/etc/init.d/mysqld stop

3. How I start the mysql server from linux terminal?

Same as #2, but with start.

4. How do I get mysql prompt in linux terminal?

Same as #1.

5. How do I login to mysql server from linux terminal?

Same as #1.

6. How do I solve following error?

Same as #1.