1968 Dart gauge help

Should the studs be wobbly or tight in their fittings without the retaining bolts that obviously will firm them up after installation.
The studs should be tight in the plate. They are press fit and should not wobble in their holes. Either fix it or replace it. I would not use it without those being secure.
That's the connection to the battery. As shown in the diagram 67Dart273 posted above, it carries all the current to charge the battery. Right after starting, that can be 20 to 30 amps although should quickly go toward zero as the battery charges up. But if the battery was run down, its going to run pull more current over a longer period of time. That's when that poor loose stud is going to cause heat and more looseness. Its downhill from there.

I will say this. Usuing a digital multimeter, two good ammeters I checked showed .1 Ohm, same as you pictured. That may be as good as it gets with a basic meter.
See here Ammeter measurements (in charging system road rage)

Also the fusible link I believe is from a later year car because the harness connector is different. I think it was changed out prior to me owning the car. I think that shouldn't be to much for concern as I think the links are the same except for the harness ends.
Yes I've seen that connector on later cars. The important thing is that the connections are good. The male terminal that goes in the bulkhead connector needs to be the correct length and not back out. That seems to be the same pretty all years that had this arrangement.