I have looked online and couldn't find a definite answer to this. My question is about if we are suppose to follow Hadiths or not?
Are hadiths mentioned in the Quran? How preserved are these Hadiths? When were they compiled and introduced?
Yes we must has to follow hadith, prophet(peace be upon him) has given us two things one is quran and second is sunnah(hadith) which every muslim has to follow.
how come you know that what is quran, and what is hadith, what is the part of quran, so whatever Prophet said that this part(wahi) is the quran that became quran and remaining is hadith.
Hadiths are phrases of prophet Mohammed peace be upon him and they describes how to perform prayer (even how many times we should do in a day), how to and when to fast (in Ramadan or other days) etc.
Hadiths are started to gathering by the companions of the Prophet Muhammad when he lives on. They are not mentioned in Quran but they describes Quran verses.
So we need to follow them with verses of Quran.
Yes we are supposed to follow prophet Mohammed -peace be upon him- Hadiths .
Hadeeths (or Hadiths) are instructions, explanation, directions that was orally said by the prophet Mohammed (PBUH). Also, it is the actions prophet Mohammed done physically or asked to be done by Muslims, in this case it called the Sunah.
In Islam we have three resources of Sharia. Sharia is the body of Islamic low. These three are:
The first two resources (Quran & Sunnah) are the basic and fundamental of the the third resource. Also, these two is all about the Constants & Assets of Islam (e.g. Prayers, Ramadan fasting, pilgrimage, and etc...) while Ijmaa is about anything else that is not fundamental in Islam.
The Holy Quran is very well preserved, protected, recorded, and conserved. If you ask any Muslim any where about a Verse (Ayah of the quran) s/he will give you the same exact words, composition, arranging of that Verse no matter what language s/he speaks and no matter where s/he lives. And in case s/he do not remember the Verse by heart, s/he will get it from the Holy Quran. So, in short it, there is only ONE Holy Quran in the whole world, and that Quran is the reference to all Muslims.
After clearing that, it is time to answer your questions:
Are hadiths mentioned in the Quran?
Yes they are, BUT it is not referencing to it as Hadiths or Sunnah. In the Holy Quran, Allah said ( وَمَا آتَاكُمُ الرَّسُولُ فَخُذُوهُ وَمَا نَهَاكُمْ عَنْهُ فَانتَهُوا) and in English the translation is:"And whatever the Messenger has given you - take; and what he has forbidden you - refrain from." So, in general, we are requested to follow Prophet Mohammed instructions, explanation, directions, and actions. Which all are known as Sunnah and Hadiths.
How preserved are these Hadiths?
To answer this question, we need to make some explanation so every things goes clear later.
So, after this short and quick introduction, let's go back to your question now, and answer it.
How preserved are these Hadiths?
They are very well preserved, and as Muslims when we hear someone saying that Prophet Mohammed PBUH said or did something we asked him, how did you know that? then he either reference us to one of these books or he provide his own "Isnad". If he reference to one of these books (especially Sahih al-Bukhari or/and Sahih Muslim) then it is most likely to be authentic Hadith, and if he provide his own Isnad, then the Muslim scholars (those they are specialized in Hadith Science) will review and verify its Sanad and matn of that Hadith (Sanad is the information provided regarding the route by which the matn has been reached) then they will categorized that Hadith relating to the authenticity of it (e.g. authentic, good, continuous, weak, suspended, hurried, problematic, and ... etc)
When were they compiled and introduced?
This is a HUGE question, which need a HUGE answer, so the best way I can help you is to reference you to page that has a good explanation about it.
Finally, I hope I could help you with your question.
No you are not obliged. You could use it to inspire you, but not as a reference as the Quran does.
Hadiths were not perfect in the sense that they were transmitted by the meanings and not literally like the Quran, and it was compiled about one century after the death of the prophet.
Someone will tell you that without hadith we will not know how to pray for example. The answer is that prayer was "practically" and unanimously learned from the prophet and transmitted to the next generations with no problem. It is like human did not wait to read about a certain fishing manual that was published to know how to fish.
We are supposed follow the prophet for the Message he transmitted unalterably, which is only the Quran.
You will find a lot of contradictions in the hadith that were falsely attributed to the Prophet (some are insulting indirectly the Prophet but considered "Sahih") to have some credibility for some political or fanaticism issues.
What I say does not mean that the Prophet is lying, it means that the hadith we read have no "objective" and proof that it sure come from the Prophet's mouth.
For example all the hadiths that talks about الغيب are to be rejected, because the prophet does not now الغيب :
قل لا أملك لنفسي نفعا ولا ضرا إلا ما شاء الله ولو كنت أعلم الغيب لاستكثرت من الخير وما مسني السوء إن أنا إلا نذير وبشير لقوم يؤمنون ( 188
Here, Allah tells him to say (<- this word is very important) that he don't know anything about الغيب and he is obliged to recognize it.
The imperative قل (say) is very important because it means that the prophet will never say something from Allah if Allah did not tell him to, this proof is sufficient to avoid considering the hadith (and particularly الحديث القدسي) are the word of Allah.
And there is a lot to say in the subject...
والله أعلم
لا ألفين أحدكم متكئاً على أريكته، يأتيه الأمر من أمري، مما أمرت به، أو نهيت عنه، فيقول: لا أدري، ما وجدنا في كتاب الله اتبعناه
and in English it means: I do not accept seeing some of you lying down and then he receive my commands which I ordered him to do or I forbidden him then he say I don't know what I found in the Holy Quran only I will follow.
ألا وإن ما حرم رسول الله صلى الله عليه وسلم مثل ما حرم الله
and in English it is: "And what ever the prophet PBUH forbidden is the just like what Allah forbidden"