[morzh]

The resistors are not a hazard. Even if badly out of tolerance. Change only those that are outside the tolerance which could be as lax as 20%.
Leave the trasformer alone if it checks out.
The Rf coils are always copper, never Nichrome if only for the reason of losses in them being undesirable and Nichrome is specifically made to be lossy.
But the insulation between primary and secondary in them is made of celluloid which disintegrates with making nitric acid as a byproduct, which in turn corrodes wires. Look for the green spots on the windings. If seeing any, even if the continuity checks out, rewind the outer winding (more often than not the inner stays ok).