So is there such limit for SQL server table? I know it can handle a lot, but is it unlimited?
Suddenly I have another curious question, for organization SQL server, employees can only access the database from work computer and organization network too.
That depends on the network topology. If you expose your SQL Server instance on the internet, anyone can access it, if they have a username and password. However, exposing SQL Server on the internet is a very bad idea.
Another curious question, how is SQL database set up? Does database always require password?
No, a database never requires a password. Normally, you authenticate to the SQL Server instance. You can do that in two ways: Windows authentication or SQL Server authentication. In the former case, you have logged into Windows, and Windows passes your authentication token to SQL Server without you specify ing username/password anew. You must however have been given access to the SQL Server instance, either directly to your login or an AD group you are a member of. With SQL authentication you specify username and password, and this is the only option if you are not logged to the domain where SQL Server is installed. Note that by default, SQL authentication is disabled.
Once you are connected to the instance, you still need be permitted to access the individual databases. You don't need a password to access a certain database, but you need to have permission, either directly to your login or to an AD group you are a member of.
But just because you have been granted access to a database, does not mean that you can do a lot in it. You still need permissions to access tables, and this access can be granted per table or on higher level. And there is different permissions for reading and writing data.
The database can be only accessed from work computer anyway (and from organization network too), employees don't really need the password. It is non sensitive database, and it can be open to all employees.
The normal way you would do this is to add an AD group that all employees are member of as login on the instance and as a user in the database. Then you need to grant the desired permissions to this group.
Finally, when you ask entirely disparate questions like you do here, it is better to post two questions.