1. The smallest ancestral graph including C, F and D also includes A and B, ie it's like NET1 with E (and all arrows going to E) deleted. No parents need to be married to make the moral graph, so we just drop directions to get the interaction graph. There is no path from F to any variable, so it's indpendent of anything conditional on anything. So clearly it's independent of C conditional on D.
2. The smallest ancestral graph including C, F, D and E is the whole of NET1. Moralising add links between the 3 parents of E (namely B, D and F). This gives us a path C-B-F. This path contains neither D nor E, so we conclude that C is CANNOT be guaranteed to be independent of F given D and E.
3. This is a bit of a plod. For each pair, find the smallest ancestral graph containing that pair. Moralise this ancestral graph, and see if you can find any path between the pair. If there is none then they are independent, otherwise, in general, they won't be. Since A is an ancestor of B, C, D and E, it's clear that the smallest ancestral graph for any pair of these will include A, and thus even without adding any lines due to moralisation there will be a path between the pair. So each such pair is not independent. E and F are not independent clearly. Finally, consider the pairs AF, BF, CF, DF. In each case the smallest ancestral graph does not include E, hence F gets disconnected, so it's independent of all of A, B, C and D.
4. Just form smallest ancestral graphs, moralise them and check to see if there is a path avioding B. You will find that AF, AC, CD, CE, CF, DF are all the pairs of independent variables.
5. A and F are not necessarily independent given E. Since E is involved the smallest ancestral graph is like NET1 but with C gone. Moralisation makes links between the parents of E. So in the interaction graph, we have the path A-D-F showing that we cannot conclude that A and F are independent given E.