What are the possible 'types' available in SQL Server as mentioned in the 'type' column in the sys.master_files view?
You shouldn't mix file extensions with file types. You have to differentiate between file extensions and what the files actually contain. 

Create Database (non-standard)

It is possible to create a database that has *.txt as the file extension for the Data files ("ROWS Data" type) which are otherwise created with an *.mdf or *.ndf extension.

It is equally possible to create a database that has a *.txt extension for the TransactionLog file ("Log" type) which is otherwise created with an *.ldf file extension.

Script to create a non-standard database

CREATE DATABASE [File_Types]
    CONTAINMENT = NONE
    ON  PRIMARY 
   ( NAME = N'File_Types', FILENAME = N'C:\SQL\SQL_DATA\File_Types.txt' , SIZE = 5120KB , FILEGROWTH = 1024KB ), -- normally *.mdf
   ( NAME = N'File_Types_01', FILENAME = N'C:\SQL\SQL_DATA\File_Types_01.txt' , SIZE = 5120KB , FILEGROWTH = 1024KB ), -- normally *.ndf
    FILEGROUP [File_Types_FS_FG] CONTAINS FILESTREAM 
   ( NAME = N'File_Types_FS', FILENAME = N'C:\SQL\FILESTREAM\File_Types_FS' ) -- no extension; is a directory where BLOBs are stored
   LOG ON 
   ( NAME = N'File_Types_log', FILENAME = N'C:\SQL\SQL_LOGS\File_Types_Log.txt' , SIZE = 3072KB , FILEGROWTH = 10%) -- normally *.ldf
GO
USE [File_Types]
GO
IF NOT EXISTS (SELECT name FROM sys.filegroups WHERE is_default=1 AND name = N'PRIMARY') ALTER DATABASE [File_Types] MODIFY FILEGROUP [PRIMARY] DEFAULT
GO


This will create a database with three files which all have the *.txt extension.

Query sys.master_files

SELECT database_id, FILE_ID, TYPE, type_desc, NAME, mf.physical_name
  FROM sys.master_files AS mf WHERE database_id = 13


Output

database_id FILE_ID type_desc   NAME            physical_name  
13          1       ROWS        File_Types      C:\SQL\SQL_DATA\File_Types.txt  
13          2       LOG         File_Types_log  C:\SQL\SQL_LOGS\File_Types_Log.txt  
13          3       ROWS        File_Types_01   C:\SQL\SQL_DATA\File_Types_01.txt  
13      65537   2   FILESTREAM  File_Types_FS   C:\SQL\FILESTREAM\File_Types_FS  


To answer your questions


"DATA Rows" will always be type 1. A file with an *.mdf extension can be of any type.
FILESTREAM integrates the SQL Server Database Engine with an NTFS file system by storing varbinary(max) binary large object (BLOB) data as files on the file system. Transact-SQL statements can insert, update, query, search, and back up FILESTREAM data. Win32 file system interfaces provide streaming access to the data. (see: FILESTREAM Overview)
Tables are stored in pages and extents inside the "Data ROWS" database files. An explanation of how data is stored can be found here: Understanding Pages and Extents and Managing Space Used by Objects.