Scanned through the Android API (reference) documentation, but didn't find specific API that allows one to achieve the following:
For the latter parts of your question, No. Imagine for a second there was, and you had an app installed that uses it. It could record your conversations and send them to a 3rd party. The app might not even disclose that it does this. That sounds like it would be a huge security problem... Don't you agree?
For #1, this is covered by marcin_j's answer
For #3, I did a bit more detailed search on this, which reveals a related Stackoverflow question and answer, which provides info on recording audio (as per the above linked apps). Please keep in mind there are likely legal requirements around recording calls.
For #4 (playing a message to the caller), the only info I was able to find on this says it is not supported. It's hard to find much more info on this with so much clutter on search coming up with apps that are basically an audio version of caller id.
Most of these answers are on StackOverflow already; hopefully bringing it all together here helps you.