I'm struggling with the same thing, my son is nearly 4. I carry our baby around with me often and when i do put him down I supervise. I have left them for a minute while I went to pee, but the last time I did that my older boy bit babies finger (he took "I just want to eat him up" to the next level). He felt awful and I felt bad for putting the pressure to "be in charge" on him. It's not that I don't trust him, but that he is still young and needs supervision and help when interacting with baby.
Your six year old is more likely to be at an age where she can understand that baby could choke (I think). Have you tried recruiting her to help. Maybe something like "I need your help showing our 4yo how to care for baby". My son is responding well to helping pick babies clothes and diaper covers. He also likes to help put dirty diapers in the bucket. In general he likes the "lets go" instead of the "stay here while I" if that makes sense.
I remember my mom had this little thing that we would use to see if a toy or object was too small for baby. Maybe you could get one and your 6yo could be in "charge" of testing things before they are offered to baby. Or maybe having a small basket with pre approved baby toys/objects. Or finding other ways to play with baby like reading or making funny faces, singing etc.
the food thing I'm at a loss for. I might try explaining why it's not ok too feed baby in a short way that can be repeated...."if baby eats this food now, he will get sick". I really don't know though.
I do think that in a way our children test us like this, I also believe that they just want to be helpful and be included. There is also gonna be a big shift and reaction to the changes in your home environment (a new baby, sharing mommy and daddy etc).
truth is you have more experience at this then I do :) I only have 2, but I'm sharing my thoughts in case it helps at all.
My son is rough with baby. He likes to squeeze his body just a bit too hard (like he can't help it or doesn't know his strength). He likes to do wild acrobatics and be physically wild while precariously close to baby. He has on several occasions hit baby accidentally doing this. I have no idea what to do or say to get him to stop. He gets angry at me when I remove baby and will sometimes try to hit me because of it (he was not a hitter before baby arrived). He may respond well to my words in the moment, but do it again a few minutes later. Any suggestions?