As the answers to another of your questions said, it is unethical to hesitate over a play when you actually have no choice, since there can be no good reason for your hesitation. The same principle applies in the situations you mention here; if, when it is your turn to play, you have a choice of cards and your decision will affect the hand, you can take as long as you need to make the choice**, with or without agreement. You are, of course, giving away the information that you have a choice to make; this may or may not be important. And if you actually have no choice, it is still unethical to imply that you have, merely because you want to study the hand; you will have to play your singleton (or whatever) and do the thinking when it actually makes a difference (such as when you have the lead).
Asking your opponents to delay play while you study dummy would actually be counterproductive; as soon as the next card is played you have more information, so your conclusions are out of date. Do your thinking when it is necessary, not before.
** As mentioned in yet another question, the time you take is in practice limited by the patience of the other players or the Tournament Director, and in some cases by session time limits. But the rules themselves make no mention of how long you can take.