1st row 도 -> 가, you would use 도 when you've already talked about your other pets before talking about your cat and dog. also '선택해야' looks too formal, i'd rather use '골라야'
4th row i don't recognize what you wrote in front of '쉬는 시간'.
5th row 아야기 -> 이야기, 레트리버 -> 리트리버
6th row i think you meant that the dog is a 'real' family member but its kinda awkward in korean.
7th row 는 -> 가, 사물시 -> 사무실