Which of the following can be determined with certainty?
I. The number of stars received by C from M
II. The number of stars received by D from O

We can note down the data from the chart into the form of a table, that gives us,

We are told that D receives more stars than C from Y. Considering Y has already given 25 stars, it will give 0 stars to C and 5 stars to D.
The only two surfers who have not given any stars to A or B is O and X, and these are the two surfers to give all of their stars to a single blogger.

We are also told that M gives different stars to the four bloggers,
Since he has already given 0 and 10, the remaining distinct stars should add up to 20. The only numbers that are remaining that add up to 20 are 5 and 15.
We know that X rewards one of C or D 30 stars and O rewards one of C or D 30 stars. Given that, M could not have rewarded D 15 stars, since Y rewarded D 5 stars, and D is also going to rewarded 30 stars by O or X, and since the total is same for all, which is 45. This is not possible.
This means that, M rewarded C 15 stars and D 5 stars.
This gives us two cases,
Case-1

Case-2

We can use these two cases to answer the questions,

There are two cases formed since we cannot identify for certain two whom did O reward the stars to, 
We can identify the number of stars rewarded by M to C. 

Hence only statement 1 can be identified uniquely.