Hoping would

Hoping would
 

Are my sentences correct?

-Ma hopes that real progress would continue to be made towards cross-strait peace and prosperity.

-Ma hopes that real progress could continue to be made towards cross-strait peace and prosperity.

-Ma thinks that it is a good chance, hoping that real progress would continue to be made towards cross-strait peace and prosperity.

-Ma thinks that it is a good chance, hoping that real progress could continue to be made towards cross-strait peace and prosperity.

Yes.

Thanks. I had the doubt because those sentences sound OK and I have seen them written like that, using would/could with the present tense of hope. Formerly my non-native teacher said with the present tense hope/hopes, we should say will/can, never would/could; do you think this rule is wrong?

Using 'will/can' gives the impression that the hope will come to pass.
Using 'would/could' adds doubt that the hope will fruition.

The tense in the main clause has nothing to do with the mood used in the secondary clause.

Excellent answer. Thank you.