Answer 1

SQL is a query language to operate on sets.

It is more or less standardized, and used by almost all relational database management systems: SQL Server, Oracle, MySQL, PostgreSQL, DB2, Informix, etc.
PL/SQL is a proprietary procedural language used by Oracle
PL/pgSQL is a procedural language used by PostgreSQL
TSQL is a proprietary procedural language used by Microsoft in SQL Server.
Procedural languages are designed to extend SQL's abilities while being able to integrate well with SQL. Several features such as local variables and string/data processing are added. These features make the language Turing-complete.

They are also used to write stored procedures: pieces of code residing on the server to manage complex business rules that are hard or impossible to manage with pure set-based operations.