CNC lathe retrofit and phase converter

Hi all -

Question #1:
I am wondering what the best approach would be to retrofit my
newly acquired Sharp 13x30 lathe to CNC. For the carriage feed,
I'd like to run a ballscrew and disengage the leadscrew during CNC
use. But, can I handle the cross-slide similarly? Could I learn
something from taper attachments? How do they work as far as
cross slide motion?

Question #2:
This lathe has a 3-phase motor, and I was planning on borrowing my
mill's VFD when needed. However, I don't know how I will be able
to keep use of the forward/stop/reverse lever on the carriage.
Has anyone dealt with this? Also, (I know this has been covered
before), if I just use a static phase converter, how much motor
horsepower will I sacrifice?

Question #3: (OT)
How are file teeth formed?

TIA,

Carlos Guillermo
VERVE Engineering & Design