Terminology is Rotary Phase Converter commonly used to turn single phase into 3 phase by essentially generating the 3rd phase through another motor and using capacitors to to phase/balance the voltage of the generated leg. It is probably the simplest approach if you do not need the additional features of the VFD.
As far as removing the control board that is your choice as to removing it or not, some people find it easier with it out. The wires are labeled as to the connections. The posted basic VFD install for the VFDis straight forward as to the pictures and detail, but if you do not have the machine in front of you it is a bit more difficult to follow. Anyway you go you will have some wiring to do unless you decide to go with the single phase 1440GT.
A brake resistor connects to the terminals on the VFD and has wires to the brake resistor which helps dissipate the excess voltage generated when braking. It is usually mounted against a flat metal surface near the VFD.
The tach. is not outputted from the VFD because it needs to read the spindle RPM not the motor, so you can buy an inexpensive tach. that uses a hall sensor and a magnet. It is a stand alone unit, I usually mount it under the DRO and also put the speed pot in the same enclosure.
You only use the inputs you need on the VFD, they can be programmed to do many functions. Typically on the basic install you want forward, reverse, jog and probably single stage or 2 stage braking (there are two sets of programming parameters for acceleration times and deceleration times.
There are many different ways to wire in the VFD, some better than others. But it is not a simple matter of connecting single phase into the VFD and connecting it directly to the machine. Machinery/the lathe can be very dangerous if you do not have the proper safety and redundancy to prevent the machine from running unintentionally.
As mentioned, single phase version the the lathe is also an option.
