Is TOAD an open-source tool for developing applications
No it's a licenced (non free) tool for connecting and working with databases.
I am planning to develop application in JAVA
I believe Eclipse is the usual free tool used for Java development
http://www.eclipse.org/downloads/moreinfo/java.php
Kindly let me know which will be best Databse for this requirement
Based on what requirements? If it needs to be free or open source, follow the MySQL and PostgreSQL suggestions, assuming it is a relational database you are after.