The yellow paste sounds like bile, and is common for dogs and pups to vomit bile on an empty stomach.
What time of day did the two bile incidents happen?
For the chew toy piece, if she is eating, pooping, playing, and being her normal self, I wouldn't worry about it, but do keep an eye on her. If she is eating then vomiting her food back out, acting lethargic,in pain, etc, she may have a blockage. That would be a vet visit ASAP.
BH, OB1, TR1, AD
Rottweiler/Hairy Dog mix?? Shelter rescue
Gryffon Vom Wildhaus