My answers are in
GREEN
1. IMM 1344
a. Person you are sponsoring (principal applicant)... Here I should put my dad's name only?? If so, do I need to fill out second form for my mom?
CORRECT, just your DAD only - pls don't fill second time for your mother because if your father will be main applicant then your mother will come as dependent
b. Sponsor person details.... Here it will be my details..correct me if I'm wrong...
CORRECT
2. IMM 0008
a. This should be filled with my dad and mom's details?
CORRECT
b. Do I need to fill out IMM 0008dep?
No need to fill out this form because in your case - your dad is main applicant and your mom will be as a dependent and you can fill her details in IMM0008
3. IMM 5768 ..... For this please correct me if I'm wrong...
a. In Question 3 -> A -> I have to mention "2" based on my IMM 0008
CORRECT
a. Here in Question 3 -> B -> i -> I have to put "1" ? (I have sponsored my wife 2 years ago and she is PR now...!!!)
In this case as she's already in Canada and this means no need to put anything here - you need to put 1 in Question# 5.. as she is your dependent
Hope this helps!