Is it possible to interface a vfd with a microcontroller to generate control signals for it?

Yes.This method is quite common.

Yes. For instance if you have a set point control module that monitors temperature from a RTD input. The controller can provide zero to 10vdc or 4 to 20mA signal to the VFD to increase or decrease to speed as required. Hope this helps.

With EtherNet and other connectivity capability, Drive Control from PLC's PAC's and DCS's is a normal mode of connection, control, management and monitoring. You can send all of your Data down one cable and receive the data you seek through the same cable. You can back that up with Analog and Digital signals from the PLC to the same drive, the options are quite simply endless.... Take care....