Okay, that's a lot of queries together, let me answer all your question on after the other.
1. I want to know the relationship between HDFS and Database
Ans: You might have got confused by the basic similarity between both which happens to be storing the data. You thought you are storing data in your database but internally the data was being stored on your local file system and when it comes to HDFS, the data gets stored in NoSQL databases like HBase using the Hadoop cluster and exploiting the parallel processing capability of Hadoop HDFS.
2. Is it always necessary to use HDFS and the data to be in NoSQL format?
Ans: First of all, Let me tell you that HDFS is designed t store any kind of data irrespective of the type of data. It can store structured, semi-structured, and even completely unstructured data. There is nothing called a No-SQL data format.
3. Is there ay specific database that always comes attached when using HDFS?
Ans: HDFS can support working with Databases like Casandra, HBase, NoSQL and many more and coming into your query, the HDFS comes with only MapReduce and nothing else.
4. Can I use RDBMS as my native database for Hadoop?
Both of these were designed to work for different environments and their functionality is also different. Moreover, there is no feature built till no to allow to use RDBMS as a native DB for Hadoop.