Why are they performed longer and to say during them?
In regards to the long Sajdah, generally it is a very good act as it has narrated from Imam Jafar Sadiq (peace be upon him) that he has said: Sajdah is the nearest shape of the human to Allah, So it could be so good for us to have long Sajdah in the Sajdah. According to a narration from the apostle of Allah (blessing of Allah be upon him and his family):
If you want Allah that you be associate with me (Mahshoor), have long Sajdah …
Although I didn't find a Hadith regarding its reason for Tahajjud, but it is a fantastic act as we saw in the traditions above. (Of course there are many Hadiths regarding its superiority that we can see some of it in the reference. Note: there must be many other profit matters regarding Ruku…)
There's a little conflict between two hadiths in the actual practice of some Imams!
One of these ahadith is telling us, that we should perform a longer sujjud (prostration) during Nafl (hadith #1 in the list below) prayers (by extending the dua'/supplication) the other is telling the Imams to shorten the prayer (#2 and #3)!
The preferred sunnah as far as I know is to do nafl prayers as a fad this means (alone) for oneself. But people used to pray some prayers in a mosque following an imam for example the tawareeh (qiyam) prayer and the tahajjud in Ramadan.
Some imams these days seem to like to show people how faithful they are or try to help the congregation to gain more concentration etc. and extend the sujjud, ruku' and dua' (dua' al qunut shouldn't take more then 1 minute!) but i heard enough scholars saying this is bida'h or at least makruh as they are imams and what they do is a kind of mura-at (مراءاة) or reya' (رِياء adulation).
1) Abu Hurairah (May Allah be pleased with him) reported: The Messenger of Allah (ﷺ) said, "A slave becomes nearest to his Rubb when he is in prostration. So increase supplications in prostrations." Sahih Muslim
2) Narrated Abu Mas`ud Al-Ansari:
Once a man said to Allah's Messenger (ﷺ) "O Allah's Messenger (ﷺ)! I may not attend the (compulsory congregational) prayer because so and so (the Imam) prolongs the prayer when he leads us for it. The narrator added: "I never saw the Prophet (ﷺ) more furious in giving advice than he was on that day. The Prophet said, "O people! Some of you make others dislike good deeds (the prayers). So whoever leads the people in prayer should shorten it because among them there are the sick the weak and the needy (having some jobs to do). Sahih al Bukhari
3) Abu Huraira reported: The Messenger of Allah (ﷺ) said: When any one of you leads people in prayer, he must shorten it for among them are the weak, the infirm and those who have business to attend. Sahih Muslim
By the way most scholars say the best is to extend/prolong the qiyam and neither the sujjud nor the ruku' and some said it's better to prolong the sujjud and ruku' for day prayers (during daylight) and to prolong the qiyam (standing) for night prayers! According to the following Hadith
Jabir reported Allah's Messenger (ﷺ) as saying: The most excellent prayer is that in which the duration of standing is longer. Sahih Muslim
This hadith can also be found in Sunan Ibn Majah and Jami' at-Tirmidi