It sunk or It has sunken would both be correct. "Can you get the leaf?" and "Can you pick up the leaf?" would have the same exact meaning here. Both would be correct and understood as a request to grab the leaf out of the water. "Can you reach the leaf?"could mean the same thing but it could also be interpreted to mean "Is the leaf close enough for you to pick it up?" not necesarily implying that you want the leaf to be picked up. It would probably be better to say "Can you get the leaf?" or "Can you pick up the leaf?"

Pick up is wrong in this context. You pick something up from a floor or a dry surface. You could use the verb retrieve or get in this case.

When the leaf reached the bottom of the swimming pool, I said “it has sunk”. I used the Present Perfect. Was it correct? - Yes, that's correct. You can drop the 'has' if you like, just saying 'it sunk'. When you say 'pick up' it usually means raising it from a surface, and so in this case 'get' would be more accurate. If it was floating on top of the water, you could use either 'pick it up' or 'get it', but since it has sunk, I would you 'can you get the leaf'.

. 'It has sunk' is correct.' . 'Can you pick up the leaf' does not sound right to me as it is under water. It sounds like an awkward concept to pick something up from a filled pool. The action of picking brings to mind a short quick action with thumb and index finger from, for example, on a tree. Or picking up something from on land. . 'Can you get the leaf?' is perfect for this situation. (I know you doubt it sounds right. It does.) . “Can you take the leaf out?” - For that to sound correct your daughter can't be in the pool too when you say it. It's sounds again, awkward. If you said that when she wasn't in the pool at the time, that would be fine. . “Can you reach the leaf?” is ok. Especially if she is at that moment trying to reach it and it is difficult to get to. None of them have the same meaning as “can you pick up the leaf?” Again, think of that as a short quick action. e'g' 'pick up your towel from the floor' or 'pick some berries fromt the vine'. I would say in most situations 'get' is your safest choice. It evokes the action of moving from where you are currently and going aquire an object or a person. Hope that helps.

You are right. I looked this word in the Cambridge Dictionary. Sank is BE. I'll try to use "sank".