Ive been learning java since last month and I wonder if theres any website that you can suggest which will force me to do a problem solving to enhance my program logic skills? Like homework or assignments from beginner to intermediate to advance. I know there are lots of tutorials out there bit I really want a homework which will challenge me. Please suggset a website which is free. thank you!

Top coder [ here
Uva Online Judge [problem archive here

there are many such.

Not sure if these sites are suitable just after one month. The thing is that you need to grasp basic from command line, to gui, simple web development and database connectivity and then just expand in area of interest through personal mini projects or by looking on or perhaps participating in open source projects. Learning new tools and ideas...
Nice that you have confidence, but one month is very short period to learn (any) programming language.
All in all I can recommend that you start actively participating on forums like this, try to help people (maybe try to solve problem on your own) and listen what others have to say