I have an Android app that's been on the market since v1 of the OS. I haven't touched it since and thus forgot all that there was to forget about developing for Android.
With the new Android 2.3 SDK, can I compile my app so that users of previous OS releases can also use it (say 1.6 or 2.1)?
Android has changed A LOT since the very first version. many things have been deprecated or aren't supported anymore. You should check what's you application is using that's not being supported now. 2.3 has got major changes in everything including the Dalvik. The things it has stopped supporting will crash if your app uses them. I would suggest a revamp of the APIs that your app is using.
Sure. Just put minSdkVersion in your Manifest.