whereu, the concious mind becomes dormant when we sleep but the subconscious mind stays awake so problem solving may continue as you say and as described by DBT9.
As for waking up, our ears still hear when we're sleeping apparently, but if not important we don't remember, but that alarm surely helps on occasion. Conversely, sometimes we sleep through exceptionally loud thunder and at other times we don't?
In the Qur'an it acknowledged ears still functioning when asleep as God had to close the hearing down " Then We draw (a veil) over their ears, for a number of years, in the Cave, (so that they heard not): (Surah Al-Kahf, 11)"
