is it possible to debug a SpringWebApplication running at a remote weblogic server?
Yes, as long as you are running a relatively recent version of
Java and you can set the command-line options (and restart) the server you can
remotely debug the application running on the server through Eclipse.
How to write a junit(from my local eclipse IDE) to test the appln running remotely?
You won't use JUnit by itself to do this - JUnit is just a unit testing framework - you'll need something that provides in-container testing (like
Jakarta Cactus) or something that makes requests through the web frontend (like
HttpUnit or
Selenium ). However, I really wouldn't recommend this, because....
because we cant deploy it locally
1.)

Why? I really can't visualize a good reason for this... Is the application specifically tied to Weblogic in some way, and you don't have enough licenses? Is it business/"security"/bureau"crazy" reasons?
2.) Unit tests shouldn't require a deployment anyway - and one of the big benefits of using Spring for DI/IOC is that your code is just a plain old java object, and can be tested in isolation outside of a "deployment only" container.