I would like to know if there is a list of these nouns and verbs (such as in the above example) or rule that will allow the..

Assalamu aleikum

May Allah increase our love and knowledge for the Quran inshallah.

In surah As Saff verse 6, there is the the noun "Yaa banii israa il". In the recitation of Hafs but not in the way of ash shattibiyyah, the noun "Banii" is lengthened 2 counts while "Israa’eel" is 4 if I am correct. This is only one example among the many in the Qur’an.
I have notice that many reciters who read in Hafs (not in the way of Ash-Shattibiyyah) know when and where to use the according mudood in this type of situation without even having the Qur’an open in front of them.

1) Therefore I would like to know if there is a list of these nouns and verbs (such as in the above example) or rule that will allow the reader to know that when reading in Hafs (not in Ash Shattibbiyyah's way) he/she needs to lengthen to 2 counts "banii" and then 4 counts "Israa’eel"?

2) If not, does the reader need to master the entire Quran and then carefully study the places where these different hamzah occur so that he/she
will not make any mudood mistake?

May Allah increase our knowledge and love for the Quran inshallah. Jazakullahi khraian.
Ma'a salam 

Answer

Wa alaikum assalaam wa rahmatullahi wa barakatuh.   Ameen to your dua’.

In tareeq at-tayyibah there are different allowed lengths for  and , and the number of vowel counts allowed for each depends on the tareeq.  One commonly read tareeq is two vowel counts for  and four vowel counts for .  As a quick review,  is when there is a medd letter at the end of a word, and a hamzah as the first letter of the next word.   is when there is a medd letter followed by a hamzah in the same word. 

In the sample cited in the question:  we have examples of both  and .  The word  ends with a lengthened [the at the beginning is not part of the word and is used for calling someone or a group] , and the first letter of the next word is a hamzah, so we have the conditions for , which would be lengthened two vowel counts if we are reading the tareeq that has two vowel counts for this medd.  In the next word, there is an alif (after the ) followed by a hamzah, and this occurs in one word, so the medd is then  which would be lengthened four vowel counts in this tareeq. 

The reader needs to differentiate between a medd letter and hamzah in one word and a medd letter and hamzah between two words to know when the medd is two vowel counts and when it is four in this tareeq.  If one can differentiate between two words, then he/she will be able to know whether the lengthening is  or .

There are a few words that are written together, but are actually two different words.  An example of this is the combination:.  There are two words, but they are written joined.  The first word is , and the second word consists of the letters written as: .  In this word combination we have both  and   .  This is because first we have a medd letter (the alif) at the end of a word , and the first letter of the next word  is a hamzah, so this medd would be .  The second word,  has an alif followed by a hamzah in the same word, and this lengthening (medd) would be .  When reading the tareeq that has two vowel counts for  and four vowel counts for , there would be then a two vowel count lengthening on the alif of  and four vowel counts for the alif of .  

For more information on these two different lengthenings, please see the following links:
http://www.abouttajweed.com/al-mudood_part_5.htm
http://www.abouttajweed.com/al-mudood_part_6_medd_waajib_jaa'iz.htm
May Allah reward you as well.

Wa assalaam alaikum wa rahmatullah.