[susan53]

1. Could be dropped or has dropped. It depends on speaker perception. Has dropped is probably more likely because it expresses a past event with a present result (the wallet is there now), but if the speaker wants to see it just as a completed past event, s/he'll choose dropped.

2. has been sleeping is most likely. It combines the perfect (past event with present result ...so he's always really tired during the day) and the progressive (= an on-going action - every night for the past few weeks). But again - it depends on speaker perception. If they just want to focus on the past event/present result they might say hasn't slept, or if they just want to focus on the on-going action might say isn't sleeping very well. That would be more likely without recently, but is a possibility.

As always, grammar is meaning. The different forms express different meanings and the speaker will choose the form which expresses the meaning s/he wants to convey - which will always depend on how s/he perceives the event.