The fact that a capacitor is marked with a 1000V label does not necessarily mean that 1000V are present on its terminal (but you should use caution). I don't think the voltage makes it out of the realm of electronics.
It's quite hard to answer your question, as the board is quite dirty and you provided a single picture. You could check for continuity and capacitance value with a multimeter


Thank you for the pics and explanations! Seeing such big power transformer in a wooden box terrifies me, probably more than it should.
For the ADC, I'm not too sure what you could use. The easy way would be to use ZMPT101B, and live with the fact that you would be using 1% of its range (you would need to check its resolution). Maybe you could also try to rectify it using an ideal diode IC.