Wow, you have some work to do I think.
The video signal is a non standard 12KHz (lowest standard is 15KHz) but there is a converter that should work.
I have 3 of these machines:
QT10N T2 1986
QT10ATC M/C T3 1987
ST30ATC M/C T3 1988
They all got original monitor and I am a little worried that they will give up soon.
So I have ordered these last week to be prepaird: (If it work I will replace them all)
Mazak industrial monitor replacement ,to VGA XVGA LCD CRT Video Converter | eBay
This should work and I know at least one person on this forum using it.
A year ago I tested a much cheeper adapter GBS8200 and that did not work and I lost the vertical sync signal and ended up buying a new card to the machine.
VGA input LCD driver board with 13.3inch L5F3 515P AG133ZJ 1 24x768 LCD panel | eBay
This monitor is a 13,3" and might be a little to big,
So if you wait a week more or so I can provide you more usefull information about this.
And there is alternatives where you can buy a plug and play monitor replacment, but the price is probably around the same that you paid for the machine.
About the batteries, you schould replace these with new before they start leaking and destroying the cards.
If you have leakage you have to clean the boards in a proper way to stop the acid.
On my machines I replaced the batteries with a holder for 3 AAA NiMh (1,2V X 3 = 3,6V) and but the hold where I easy can change these in the future. (Cables to the boards)
You will have 2 or 3 batteries to replace depending on what version of boards you have.
These batteries holds the parameters and program in memmory when it turned off.
Hopefully you have these parameters in one of your books and they look like these:
The day you start enter all parameters you have to know that the binary number (8 1or0) has to be entered with a parity number with the amount of 1, like this:
1100 0010 = 110000103
1111 1111 = 111111118
0000 0000 = 000000000
I think you will find all the help you need to get this machine running here at this forum.