B. Him Singing. Such an odd question
I don't believe that any of these are run-on sentences. This is because they all possess some form of punctuation, which creates a small to moderate oause in the sentence, allowing for the person reading to breathe in between, and preventing a run-on sentence.
i believe the answer is
a) greasy and soapy
unctuous: (chiefly of minerals) having a greasy or soapy feel
Tamara or her brother needs to take the dog for a walk.
Hope this helps.