A person entered water with a sheretz floating in it. He is unsure whether he touched the sheretz. Is he impure?
Halacha 3 (ch.14): doubt about floating sheretz in water is ruled pure — even if there is only just enough space for the person and the impurity.
Question 2
Impure liquids were on the end of a stick and someone threw it among pure loaves. Doubt whether the liquids touched the loaves. What is the status of the loaves?
Halacha 7: doubtful whether impure liquids touched an object = pure for the object. However, if an impure person extended his hand into liquids = impure.
Question 3
Both one's hands were pure. There were two loaves before him — one pure, one impure. He touched one but doesn't know which. What is the status of his hands and the loaves?
Halacha 11 (ch. 14): doubt about hand impurity — whether contracting it, transmitting it, or purification — is always ruled pure. Everything stays as it was.
Question 4
A doubt about impurity arose in a private domain involving an entity that has no capacity to respond to questions (a vessel). Is the vessel impure?
From the summary of the 12 doubts: all twelve are ruled pure even in a private domain specifically because the objects lack the capacity to respond to questions — the private-domain stringency applies only to persons who can be examined.
Question 5
Two domains have an impure and a pure object. A person touched one but doesn't know which. What is his status?
Halacha 9 (ch. 14): doubt involving two domains (an impure entity in one and pure in another) where it's unknown which was touched — is pure, and is included in the twelve doubts ruled pure.