Everything below is assuming the opponent uses a normal shield, not a lightshield. I'm having trouble finding any data on those but have been told advantage permutations on lightshield are different.
I feel like I always get punished for FC Nair---> Dtilt on someone's shield... Should it work, but I'm just messing up on spacing or something? Or is it pretty punishable with shield grabs (which is usually what happens to me)?
Behold the magic of numbers! Best possible advantage on block for f/b/n-air is 4 (with a frame perfect float cancel from a ground float). D-tilt hits on frame 12. Most good grabs in this game hit frame 7. The worst standing grabs in the game hit frame 18 (Samus and Yoshi). On the other hand Samus can still WD OOS. Also worth noting is that grabs win vs any hitbox if a grabbable hurtbox is within range, and some moves extend Peach's hurtbox (this applies to many many moves for the whole cast, notably d-tilts).
So no, FC anything -> d-tilt is not "safe" on shield. At least not frame safe.
Samus is one of the only characters who can't grab on time.
Tether grabs (also Zelda) are crap and will be beat out by the d-tilt. Many grabs which would win framewise are out of range following the fair. Nair not quite so great with the range.
A caveat is that Shield SDI is slowly being improved by players like S2J, Armada (I'm pretty sure I've seen him shield SDI vs. spacie shield pressure to get lolwut grabs), etc. Peach's aerials (other than dair) are not short on hitlag, so don't expect the space between her and the shielding opponent to be consistently out of grab range. Adderall son. Its like vitamins for fox.
Fair to d-tilt is cool as a mixup though. Just remember that you can aerial on shield and dash grab, and it will work far more consistently than d-tilt (having roughly half the startup lag).
Hope that excessively answers the question.
Do any of you know about partial CCing, lightshield adv or that in between lightshield and normal shield adv? I've noticed all of these things in testing and they don't seem to be common knowledge. Help?