questions regarding DC motor rotary encoders and a coil

I am working on a project, its an upcycle project involving a plotter (1993). I want to use an arduino or arduino based board (like a KFB2.0) to replace the original board on this plotter and drive the 2 DC motors with encoders and the pen carriage Z Axis. the Z Axis is a simple coil that stays up and is driven down when current is applied. on the end of the pivot is a HEDS 9001 encoder. I found a pinout of the encoder and have determined with the Uno that it works. I have also gotten the encoders from the motors to work with the Uno and used the serial monitor to read the encoder. I have stepper drivers for the KFB2.0, a Duo on the way with a L298N as well. My questions are:

  1. can the arduino/KFB2.0 or Duo make a suitable replacement for the original board to run this plotter?
  2. can the arduino etc. drive (with proper drivers) DC motors with rotary encoders?
  3. what would i have to use to get the Z Axis to move up and down using the encoder?
  4. can the L298N driver work for that?

I am learning as I go, and appreciate all the help, and suggestions