[Disclaimer: this answer was written before I saw Robominister's answer. It contains similar advice, but I'm posting my answer, nevertheless.]
Well done, Aditya! Yes, QuadBatches are for sure the best way to display tile maps in Starling. That's the most efficient way to do it!
As for your questions:
1) I guess you are using Starling 1.5.1, right? In the latest Starling version (soon to become v1.6), you'll get a more useful error:
[Fault] exception, information=Error: Exceeded maximum number of quads!
The maximum number of quads per QuadBatch is "16383" (that's a limitation of the buffer sizes of Stage3D). If you need more than that, you have to create a new QuadBatch for that layer.
2) The solution you found is the right one! "readjustSize" is the way to go.
3) To further optimize this, you would need to find out which quads are visible at a certain time. For this you, *cannot* simply iterate over each of them and find out if they are in the visible area; this would take up far too much time.
I'd do it like this:
A layer could have a property like "visibleArea", which is a Rectangle that defines which part of the map is currently visible. In the first frame, you add only the quads that are within that area (which is simple if it's a regular grid; no need to iterate over all quads).
Each time the camera moves, new tiles will come into view, and others can be removed. The trick is to efficiently add and remove those tiles, and to only make an update when there is a change.
Since we're talking about a QuadBatch, and not a normal Sprite, this is a little tricky, though. Probably it would be best to simply reset the batch when the visible quads are changing, and add all that are visible at that time. That should still be very fast. (Normal batching does just this, all the time.)
If that's worth it depends on your use-case. If the map size is somewhat reasonable, just stick with what you have now (having all tiles in the QuadBatch at once). The GPU will do the clipping for you, anyway. In other words: if it's already fast enough, it's fine.