First of all you should know that the Messenger of Allah (Peace be upon him) warned his companions not asking too much (for details) as did banu Israel, so that their ahkam (of shari'a) became "difficult" to apply. See for example in Sahih Muslim.
What type of questions where they asking?
Ibn al-'Arabi in his tafsir gave 4 possible reasons for the revealing of the quoted first part of Verse (5:101) :
- a narration from Sahih al-Bukahri, Sahih Muslim, Jami' at-Tirmidhi and others where a man asked: "Who is my father?" ...
Note that the answer could be very embarrassing for his mother, if she had premarital sex in jahiliya, especially as this was asked while the Messneger of Allah (peace be upon him) was holding a speech!
In Tafsir al-Baghawi, ibn Kathir and at-Tabari different narrations where quoted with the reaction of the mother of that man who asked about his father, where she calls her son a disobedient, who compromised his mother (here the Arabic statement from tafsir al-Baghawi):
ما سمعت بابن قط أعق منك ، أأمنت أن تكون أمك قد قارفت بعض ما تقارف نساء أهل الجاهلية فتفضحها على أعين الناس؟
- an other narration from Sahih al-Bukahri (also in al-Awsat of Imam at-Tabarni) which says that people asked the Messenger of Allah about things to mock him.
- a narration which is not in the two Sahih books, but in al-Mustadrak, in Sunan ibn Majah, in Jami' at-Tirmdihi, which says that the companions (May Allah be pleased with them) have asked if Hajj is required every year, but the Messenger of Allah (Peace be upon him) remained silent!
- a quotation of ibn 'Abbas (May Allah be pleased with -both of- them): saying it's about people who asked the Messenger of Allah (Peace be upon him) about al-bahira البحيرة(a she-camel whose milk was spared for the idols and nobody was allowed to milk it), as-saa-iba السائبة (a she-camel let loose for free pasture for their false gods, e.g. idols, etc., and nothing was allowed to be carried on it), al-Wassyla الوصيلة (a she-camel set free for idols because it has given birth to a she-camel at its first delivery and then again gives birth to a she-camel at its second delivery) and al-ham الحام (a stallion-camel freed from work for their idols, after it had finished a number of copulations assigned for it, all these animals were liberated in honour of idols as practised by pagan Arabs in the pre-Islamic period) who are quoted in (5:103).
then he added that
if they are shown to you, will distress you
makes the first reason stronger, because if the Messnger of Allah (Peace be upon him) answered that son (in some ahadith he didn't answer) then maybe his mother would be embarrassed with what she had committed in Jahiliya!
He also quoted a Haidth from Sunan ad-Daraqutni, al-Awsat of at_Tabarni and zwaid al-Haythami which he qualified as sahih and supports the 3rd possible revealing reason and also goes ahead with the first hadith i quoted in my answer:
إن الله أمركم بأشياء فامتثلوها ، ونهاكم عن أشياء فاجتنبوها ، وسكت لكم عن أشياء رحمة منه ، فلا تسألوا عنها
My Translation (please take it with care)
Allah ordered you to observe things, so comply with them, and He has forbidden you things so refrain from them, and He remained silent about things to mercy from Himself, so don't ask about them!
So his conclusion is -apparently- that things which are forbidden to ask about (according this Verses) are things where the answer would hurt or bring any kind of distress once it's spoken out or revealed! For example if one knows that his mother had premarital sex or if we should practice hajj each year, or maybe a Question with a nasty result could apply to this like the Verses from (2:55)! He also insisted in explaining that (fiqh) calamities النوازل are excluded from this Questions one shouldn't ask, as some people used a hadith to hinder people form asking extensively about fiqh matters!
- Some scholars (Fatwa in Arabic) said that Question about
irrelevant/useless things are included in this. But this doesn't mean
that asking to seek knowledge is forbidden (16:43). And you'll
find examples of that in the Qur'an for example in (2:189),
(2:219) and (2:222)...
Imam al-Qurtoby in his tafsir concluded after quoting ibn al-'Arabi's reasons:
وفي الصحيح والمسند كفاية . ويحتمل أن تكون الآية نزلت جوابا للجميع ، فيكون السؤال قريبا بعضه من بعض ، والله أعلم
- - - (My own transaltion take it carefully) - - -
And what is in the sahih with a connected (sane) narrator chain should be enough. But it is possible that the verse is an answer of all of these reasons too so the kinds of questions might be similar to each other (or asking question might be meant in general) And Alalh knows best!
Why or how the answers would turn them into disbelievers?
According to tafsir at-tahrir wa-tanwir (5:102) refers to people of the book who asked their Messengers and Prophets (Peace be upon them) about some details of subjects and once they were given them they didn't believe: For example Thamud who asked Salih (peace be upon him) about a sign from Allah so once Allah brought out a She-Camel from the rock they hum-strung it! Also some tafsir's mention as an example the table of the disciples of 'Isa (peace be upon him).
Other narrations which are considered as related to this Verses
- In most tafsir books other narrations are quoted like this one from Sahih al-Bukhari, where the Messenger of Allah (Peace be upon him) one day allowed his companions to ask him anything as long as he was in his place.
- A longer narration from Sahih Muslim, about the man who asked about his father with the addition of a narration with the reaction of his mother.
- An other narration from Sahih Muslim defining that the greatest sinner among Muslims is the one who asked about something Allah didn't forbid "until" Allah forbid it because of his persistence!
And Allah knows best!