Would plating a coin make it overweight by a measurable amount?
Not by a measurable amount, no.
Would the details of the coin be as sharp on a coin that is plated or does the process fill in the finer details?
That depends on how the job is done, and for how long it sits being plated. If dipped or plated by electralosis for a longer time, the detail loss would be somewhat substantial. If plated by electralosis for a very short time, the coin would still change color, but wouldn't have enough on it to make any measurable difference and would not affect the details at all.
What metals would make a coin look like gold, besides gold?
None that I can think of. Plating a dime in gold involves only a couple of grains of gold, less than $5 worth even on today's market. Using electralosis uses an unmeasurable amount of foreign metal (gold in this case), which wouldn't involve anything more than a gold ring or something made of gold, and it wouldn't effect the ring or piece of gold enough to make a difference.