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What does "no digit may be composite" mean, that all the digits have to be prime numbers?
If so, then 9 is composite, and 8 is composite, but 7 is prime, so the (trivial) answer is 777777. Any other number meeting the criteria given is smaller.
This is so glaringly obvious that I can't help thinking you meant something else. You might want to ask again, but be more specific next time.
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What is the largest three digit number if no digits may be repeated?
The largest number with no repeated digits is 9,876,543,210 although it is 10 digits long, the largest 3 digit number with no repeated digits is 987
What is the biggest number you can make using the digits 935and 1?
That depends a lot on how often you may repeat each digit, and what operations are allowed. If you just want to write a four-digit number, using each digit once, start by writing the largest digit on the left, then continue with the second-largest, etc.
When dividing a 3 digit number?
Any time. There are no restrictions on when you may or may not divide a 3-digit number!
Do you always get a prime number when you rivers a two digit prime number?
No, and you do not even if you reverse them.
When a composite number is divided by 9 then is its quotient prime?
May not be, The quotient may or may not be prime.
