During the time when you were away Elis was looking after your dog. YES this one is right
He caught a cold through drinking cold water.
added ( a) in to make this right, but you can not catch a cold from drinking cold water it is a virus,
Do you get a let for your house? I am not sure what you mean? are you referring to renting out a house?
He is said to have gotten married ten times. changed got to gotten
What withheld you from coming to school? another way would be :what kept you for coming to school. that would be how an english speaker would say this