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Question

ASSALAAM U ALAIKUM

 I AM STUDYING TAJWEED AT THE MOMENT AND I NEED YOUR HELP ON TWO DIFFERENT MISCELLANEA WHICH I HAVE GIVEN BELOW. JAZAKHALLAH KHAIR

1.  In these four words Idghaam will be Naqis (incomplete)

That means that the makhraj of the  will be incorporated into the  but not the sifaat of  Istiela and Itbaaw, hence the  will be read with tafkheem, but without Qalalah. 

2.  In Surah Yusuf the word  has to be read with ishmaam or raum.  When making Ishmaam, idghaam has to be made, and when making raum, izh-haar has to be made. 

Ishmaam means to indicate by the lips towards the dhamma.

Raum means to read one third of a harkat.

 Answer

Wa alaikum assalaam wa rahmatu Allahi wa barakatuh,

1. We are not sure what is it that you need assistance on, but will clarify some points in the portion of the lesson you sent.  The  does merge incompletely into the  in the four words given in number one.  This is called , and what remains of the  is the characteristic of  only.  The  and  share the same makhraj, or articulation point at all times.  The  will be read, but with  of the tongue to the roof of the mouth for the first   of the shaddah.  Please also see the lesson on the idghaam mutajaanisayn.

http://www.abouttajweed.com/al-mutamaathilayn.htm

2. The word   can be read two ways in the reading of Hafs 'an 'Aasim min tareeq Ash-Shatibiyyah, one of the two ways is with idghaam of the two  (hence the shaddah), with a circling of the lips with no sound () as an indication of the dhammah on the first , since this is a "kabeer" idghaam, meaning both letters of the idghaam have a vowel. 
The second allowed way of reading this for Hafs 'an 'Aasim by the way of Ash-Shatibiyyah is with ith-haar, of both of the two letter , as in: , but with ikhtilaas () or stealing of part of the vowel of the first .  The amount of the vowel that remains is 2/3 in .
Please also see the following lessons:

http://www.abouttajweed.com/al-mutamathilayn_al-mutajaanisayn_4.htm

http://www.abouttajweed.com/new_page_11.htm

Wa iyyakum wa-l-muslimeen