Question 1
Before the start A and X are sailing close-hauled towards a pontoon. X calls for room to tack. A replies 'No, you can go inside'. X protests. What should the call be?

Answer 1
Rule 19.1 allows X to hail for room to tack to avoid the obstruction. It is up to X to decide whether to tack or gybe to avoid the obstruction. A breaks rule 19.1.
Penalize A.

Question 2
The situation is the same except that X by luffing slightly is able to avoid the pontoon. X calls for room to tack. A replies 'No, you can luff slightly'. X does this and protests.
What should the call be?

Answer 2
Penalize both boats. Rule 19.1 only applies when the hailing boat is sailing close-hauled or above and needs to make a substantial alteration of course to avoid an obstruction. Because she does not need to make a substantial course change to avoid the pontoon, X breaks rule 19.1 when she hails. However a hailed boat must assume such a hail is valid, and respond to it. By failing to do so, A also breaks rule 19.1.

If instead A tacks and protests, then X breaks rule 19.1 and A breaks no rule.