1 - When you think they're going to take an action that would beat your WC, whether that's a late B/F3, jumping, etc. My preferred option after cancelling a WC is D2. If they jumped, then it catches them. If they stayed on the ground and blocked, then I'm punishable but they'll have to react quickly to the situation and punish. Another WC immediately afterwards in case they're late on the punish tends to dissuade them from trying to punish D2 even though it's pretty minus on block.
2 - IMO Grundy deals fine with rush down, or at least ground-oriented rush down. To attack Grundy on the ground is risky, because there's a possibility that he'll WC, armor through your entire string, and then punish for ~54% for 1 bar and get the trait buff of his choice. Lots of strings have a small gap in between hits (like Lantern's b1->2/3 followup) that you can MB Trait, MB B/F3 (if you have perfect timing you can do this in between 1-frame gaps but it's pretty tricky), or Walking Corpse through so it's hard to pressure a Grundy that's aware of the gaps in strings.
3 - If you cancel into Trait off a blocked D1 it grabs them, so I'm confused by your first statement. The only safe thing after D1 is MB Cleaver, but as Gruff pointed out above you can be grabbed out of it, so technically the only safe option is to just block after D1. If your D1 hits, then I generally go for another D1 cancelled into Trait to catch them blocking. Next time I cancel MB Cleaver or WCC to catch them jumping out of the previous setup. After you hit them with one each it's just reads.
4 - D2 leads to more reward (about 45% for 1 bar IIRC) and is great for hitting opponents that are trying to cross you up. Crap horizontal range, takes some time to actually hit above & behind him (8 frames is only to the first active frame in front of him, to stop crossups is closer to 11/12 frames), and is relatively slow to start up compared to the grab though, so use with caution. AA grab only gets you ~12% and oki but has a better hitbox and psuedo-invincibility, making it a safer option.
