1.what are the three styles of recitation? 2.what are the two types of mistakes in Quranic recitaion (with detail)

Questions and Answers
 1. What are the three styles of recitation?
 There are three speeds of recitation ( not often referred to as styles) are Tahqeeq (slow), tadweer (medium), hadr (fast). 
http://www.abouttajweed.com/31100101.htm


2 . What are the two types of mistakes in Quranic recitaion ( with detail) 
The clear mistake (lahn jalee) such as changing one letter into another, changing the vowel, etc  and the hidden mistake (lahn khafee) such as missing a tajweed rule like the idghaam or ikhfaa'. 
http://www.abouttajweed.com/kb/entry/185/
http://www.abouttajweed.com/kb/entry/314 /

3. What are the major differences between : qad3, waqf, and sakt?

We believe you mean qaT3, which is cutting off of recitation, .   QaT3 is the cutting off of recitation and leaving it to do something else.

The waqf is stopping for a short period of time and taking a breath and returning to recitaiton. The definition is: Cutting of the sound at the end of a word, usually for the period of time of breathing, with the intention of return to the recitation, not with the intention of abandoning the recital.

The sakt is a breathless pause defined as: Cutting off the sound for a time less than the time of a stop, without breathing, with intention of returning to the recitation immediately.

4. isti3aatha is preferred at...? basmallah is obligatory at...?
 isti3aatha is preferred at the beginning of recitation.
 The basmalah is obligatory at the beginning of a surah, except surah At-Tawbah. 
Please see:
http://www.abouttajweed.com/seeking-refuge-and-the-basmalah-in-recitation/seeking-refuge-and-saying-the-basm.html

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