IVM sounds like a good solution for you.
1) As far as I know there are no difficulties running the software on 2003, but I haven't tested this myself, so you may want a second opinion.
You have the option to run IVM as a service, run it on startup (login to account), or to run it manually.
2) I happen to also be a Vonage user and I am using a Linksys Sipura 3000 / 3102 FXO adapter to convert the analogue line from the Vonage ata adapter into a VoIP line that the IVM software can work with (using Axon software, which is free) and this works well, although is slightly inefficient because essentially the voice data is going from Digital Voip to Analogue back to Digital Voip. The alternative is to purchase a softphone line from Vonage that can be connected directly to IVM or Axon (Unfortunately Vonage only has limited plans for them and the service also requires that you also have a Vonage main line as well). Don't hesitate to ask if you want more information.
3) Yes, IVM can be configured to dial out on another line during a call and transfer calls to that line or to another extension on the phone system. I haven't tried transferring from a VoIP vonage line to an Analogue modem line (usually I just transfer from one VoIP line to another), but I can't see why it would cause a problem, again you may want a second opinion.