I can be wrong in some points but anyway...
- does it support transparent backgrounds (see my prevous topic about DTV) ?
It depends on the hardware... I believe that some cards allow rendering to texture with alpha channel nowadays.
- does it support 3D text like Java3D ?
No. LWJGL is a low-level API. Conserning graphics it's just OpenGL wrapper (you can think that graphics part of LWJGL simply means OpenGL). So the question could be: "does OpenGL support 3D text directly?". The answer is no but it's possible to provide this functionality on top of the library.
- can I use Java2D to write over LWJGL buffers ?
No. LWJGL has no connection with AWT. But you can use Java 2D to draw in a BufferedImage then use the pixels as a texture and draw textured quad to the buffer.
- can I save single animation frames from LWJGL ?
Yes, it's the same as for OpenGL. For instance, render your frame then grab the pixels by using glCopyPixels() and save 'em on disk in desired format.
- does it support field-rendering (I mean odd/even video fields) ?
Does OpenGL support them?
Note that LWJGL is a low-level API. It (OpenGL) has most of necessary features for developing a video-editing software on top of it. At the moment there is no such software using LWJGL so you have a chance to be a pioneer in this field!