automatic fluid level is always checked in running engine because when you shut it off half the torque convertor drains out. Be sure you check it at warm temperature - automatic trans should never be run hard when cold, meaning if you have removed the thermostat valve and have direct cooling fan it will take a very very long time to warm up.
Fill with ATF DX3 or 2D - its not very expensive.
btw dont try to judge engine temperature by feel, 90C will burn you badly. Always have the thermostat in place and the temperature gauge working. btw what transmission did you install? there are two variants, one is a fully hydraulic type that has a speed governor and one is an electronic type that requires a TCU to shift, both look exactly alike - except for a bunch of wires.
if you have proper shifting then Im assuming that you have the old style hydraulic which is correct.
and go to a proper mechanic and ask him to make proper foundation brackets.