1) You'll need more than just a basic license sine that license does not permit any OGMs. The OGMs (out-going-messages) are what drive your call-flow applications. They play recordings, collect and process user input. Without any OGMs, your system would just be an answering machine. You'll need a bare minimum of the small business license, still with only 3 OGMs, there is not much room to play with.
It is possible for you to use one IVM installation for a system of operators however, so you can do that to save on costs and upgrade to one of the higher Interactive or Enterprise licenses.
2) There are some professional telephony boards that support 4, 8 or even 16 lines on a single PC (usually a maximum of 4 lines per card installed on the PC). Compared to voice modems, telephony boards are much more expensive however. You are correct that most voice modems only support 1 line.
Voice Modem / Telephony Board Comparison
1 Line per card / up to 4 lines per card
Average voice quality / Better voice quality
Suitable for answering machines / Can be used for all sorts of applications including integration with a PBX for call routing and transfers
3) If you are using a digital PBX such as Axon or Asterisk, you'll need to connect the phone lines using either
a) Telephony Board
FXO Adapter
A Voice Modem would not be suitable for this application. Telephony boards are discussed above. FXO adapters essentially convert your analogue line into a digital VoIP line that can interface with IVM and most digital IP PBX systems. FXO adapters are not too expensive however usually only support 1 line per device. Each FXO adapter requires a free Ethernet port on your network and requires some time to configure properly.