By "hazard/turn signal relay", I assume you mean the flasher. Did you buy a "mechanical" flasher, as was originally supplied, or an electronic one? Honestly, the electronic flashers solve a lot of turn signal problems on these cars. The mechanical flashers have to handle exactly the right amount of current to a) flash and b) light the dash indicator. The electronic ones are indifferent to current. The issue is that with 50 years of oxidation on the bulb sockets and harness connectors, the resistance rises enough to reduce the current low enough to create problems with the mechanical flashers.
There are lots of threads here, as well as on 2002faq, about flashers and turn signals.
Not quite sure I understood that. What size tires are on it now? If they're not 14", my instincts would be to run the tires that are on it for awhile while you are searching for period-correct, 14" wheels. I love the original, 5-spoke wheels, but others like the Alpina style. And yes, the choices in 195/70-14 tires are limited; such is the price of beauty.