For the moment, I suggest you forget about 'Neutral' and 'Hot' connections for the moment - and just
categorically determine the configuration
and state of the transformer.
Since you have pulled the cover off, I take it you have confirmed the yellow was, indeed, connected to the case. That is good. We can forget about that one for the moment.
We now have only 3 connections to worry about - and from the
printed label, it is clear we should expect an autotransformer inside. The
hand written label noting 2 x 110V is a bit misleading - and while I could describe how someone might put it there, it is just going to muddy the discussion ... so let's just ignore that for the time being.
However .... about those 3 connections.....
So far, it seems likely that it has a shorted winding.
This is something I have felt ever since this comment:
red-brown are 0.3ohms and red-black are also 0.3ohms.
black and brown are a dead short.(0ohms)
That just isn't right for a CT transformer with two equal halves. You were absolutely right when you said:
CT should have exactly or close to half the resistance of the other two right?
But then you added:
Makes sense to be 0ohms if the other two are 0.3 .....
No. It does
not make sense. Just try drawing two resistors joined at one point to give the measurements you have observed. (I think I can see where your statement comes from - and if I do, you have swapped a couple of things around.)
To me, the only configuration that makes sense of those readings is if there is a dead short across a whole half of the winding (ie between two connections.)
Now that you have opened the can and we can see the transformer windings, the physical construction would strongly suggest the inner and outer connections are the ends of the winding with the one in the middle being the centre tap. That being the case, if I were to label the connections as I, C and O for inner, centre and outer) we should have:
R
IC = R
OCR
IO = R
IC + R
OCHowever, at these low levels, I am hesitant to rely on such resistance measurements with a regular DMM. What I would suggest is applying a voltage - with some current limiting - across the inner and outer terminals and take some
voltage measurements. You are going to get much better resolution trying something like this - and then doing a bit of arithmetic: