I just bought a matching tie clasp/ cufflink set. Do I wear them together, or would I look like I was a five-year old whose mother dressed him?
My dad always wore his together, I thought it looked sharp. My vote is yes, wear them together.
Absolutely, provided that the tie clasp is nothing more than a narrow bar and not something that draws away from the tie too much. Also make sure that you wear it about sternum level, any lower and it’s not a good look.
I would say…wear the cufflinks, but not the tie clasp. Ever. I don’t care for them…I think jewelry should be mostly functional on a guy, and while tie clasps are supposed to be functional, I don’t think they are really necessary, and they tend to look as though the guy just really likes jewelry and is trying to sneak another piece in.
If you really like to tie your tie down, though, I definitely would not do the matchy-matchy thing. I would get a couple very plain, rather unobtrusive tie clasps, one in gold and one in silver and always wear one of those, no matter what your cufflinks look like.
Thank you all for your help! 
Skip the tie clasp. Tie clasps fall into the same category as flip-up sunglasses, umbrella hats, and socks with sandals: Somewhat functional, but not fashionable.