No, I haven't rebuilt a tuner, ever. But I can answer some of your questions.
1) The selenium should be disposed of properly, it is toxic. You can put in a diode. Just verify the voltage rating and the current rating.
2) Try Antique Electronic Supply (
http://www.tubesandmore.com/) or Angela Instruments (I couldn't get the link to open) for the caps. An alternative is to leave the can and put modern electrolytics under the chassis. DO use a slightly higher voltage rating than specified. The tuner was built when 110V was the norm, 125 is close to the norm today. That is a 13% increase.
3) Carbon comp resistors are notorious for noise and changing their value with heat cycles. These are a bad thing in tubed designs. But that is what was available when the tuner was built. There are people who like the sound, but it is more the circuit becoming out of spec than anything else.
Metal film is a good replacement. If you can determine what resistors are in the signal path you can substitute "designer" resistors.