Is Sujud At-Tilawah Obligatory?
Question

When is it obligatory for a Muslim to prostrate? What should we do? Is it permissible to listen to the Quran when we want to sleep, i.e., if the recitation of Quran continues when I am asleep?
If I am listening to the Quran on the computer and I hear a verse in which a prostration is required, what should I do? In Surat Maryam, there is a verse which says that when we hear the verses of Allah we should fall down prostrating and weeping.
Praise be to Allah.Verses of Sujud At-Tilawah in the Quran
There are fifteen places in the Quran where the prostration of recitation is required. 
Is Sujud At-Tilawah obligatory?
The prostration in these verses is mustahabb for the reader and the listener, and it is not obligatory. If a person wants to prostrate he should say takbir , then say in his prostration what he says when he prostrates in prayer, then get up without saying takbir or tashahhud or salam. If the prostration of recitation comes during a prayer, then he should say takbir when standing up again. 
Can you listen to Quran while sleeping?
There is nothing wrong with a Muslim listening to Quran when he wants to sleep , rather listening to Quran will give him peace of mind and help him to relax. Allah says (interpretation of the meaning): 
“Verily, in the remembrance of Allah do hearts find rest.” [Al-Ra’d 13:28]
Should you offer sujud al-tilawah if you are listening to Quran from a recorder?
With regard to doing the prostration of recitation when you are listening to a verse in which a prostration is required on the computer or a recorder, it seems that it is not required to prostrate for that. The earlier scholars discussed a similar matter, as is mentioned in al-Fatawa al-Hindiyyah (1/133), which is a Hanafi book: 
”If he hears it (a verse in which prostration is required) in an echo from a far-off place, then he is not required to prostrate.”
This is akin to hearing it on a recorder and the like. 
Shaykh Ibn Baz (may Allah have mercy on him) was asked: 
If a person is listening to recitation of the Quran on a recorder, and the reciter recites a verse in which there is a prostration of recitation , should he prostrate? 
He replied: 
“It is not prescribed for the one who is listening to prostrate unless the reciter prostrates, because Zayd ibn Thabit recited Surat al-Najm to the Prophet (peace and blessings of Allah be upon him) and he did not prostrate, and neither did the Prophet (peace and blessings of Allah be upon him). This indicates that the prostration of recitation is not obligatory, because the Prophet (peace and blessings of Allah be upon him) did not rebuke Zayd for not prostrating. The hadith also indicates that the listener should not prostrate unless the reader prostrates.” (Majmu’ Fatawa Ibn Baz, 11/415). There is a similar comment in al-Sharh al-Mumti’ (4/133). 
Is it recommended to weep when reading the Quran or listening to it?
With regard to the words of Allah in Surat Maryam (interpretation of the meaning): 
“When the Verses of the Most Gracious (Allah) were recited unto them, they fell down prostrate and weeping” [Maryam 19:58], here Allah praises the prophets and messengers and those whom Allah guided and chose for their perfect fear of Allah and their humility before Him: when His verses were recited to them, they fell down prostrate and weeping. 
Hence the scholars described it as mustahabb to weep when reading the Quran or listening to it. ‘Umar ibn al-Khattab (may Allah be pleased with him) used to say when he read this verse: “This is prostration, but where is the weeping?” – rebuking himself (may Allah be pleased with him) for not weeping. 
Allah has described those to whom knowledge was given, when the Quran is recited to them (interpretation of the meaning): 
“Say (O Muhammad to them): ‘Believe in it (the Quran) or do not believe (in it). Verily, those who were given knowledge before it (the Jews and the Christians like ‘Abdullah bin Salam and Salman Al-Farsi), when it is recited to them, fall down on their faces in humble prostration.’ And they say: ‘Glory be to our Lord! Truly, the Promise of our Lord must be fulfilled.’ And they fall down on their faces weeping and it increases their humility.” [al-Isra 17:107-109]
We ask Allah to make us among those who truly fear Him. 
And Allah knows best.