Wa alaikum assalaam wa rahmatullahi wa barakatuh. Jazakum Allahu khairan.
Yes, there are rules for pronunciation of two saakin letters meeting, such as when the tanween ( saakinah) meets the saakin letter that follows the non-pronounced hamzah al-wasl when continuing reading. We only use the hamzah al-wasl when starting a word. If we are continuing reading, meaning not starting on the word beginning with hamzah al-wasl, it is ignored and we read directly the letter that follows it, which is always saakin.
A criticism of the musaahif printed in the Indo-Pakistan region and used widely is that they write in the vowel that is acquired on the tanween not on the tanween, but on the hamzah al-wasl with a small . This is not correct in that the hamzah al-wasl does not have a vowel and is not pronounced in this case and the that has acquired a vowel is the noon saakinah of the tanween. Since this is a temporary vowel and is due to the transient condition of a two non-voweled letters meeting, the Medinah Press Complex does not write in anything.
When two saakin letters meet, between two words, the first letter acquires a vowel to eliminate two saakin letters being pronounced after each other, something that is difficult. The rules for this can be found at the following link: http://www.abouttajweed.com/121003.htm
All the different rules for different combinations can be found at the above link. In the case of the tanween, the saakinah of the tanween acquires a temporary kasrah when followed by a saakin letter. Examples are as given in the question:
The last statement in question D 2 above is correct when there is a tanween followed by a words starting with hamzah al-wasl and all the transliteration examples in D2 are correct. In all these cases of a tanween followed by a saakin letter, the hamzah al-wasl is not pronounced, and the noon saakinah of the tanween acquires a kasrah. If we are starting on the word that has a hamzah al-wasl, we then use the hamzah al-wasl and employ the vowel is determined by the lessons on hamzah al-wasl in the following link: http://www.abouttajweed.com/the_hamzah_al-wasl_lessons.htm . Hamzah al-wasl can have any of the three vowels and which vowel we use is explained in the link on the hamzah al-wasl lessons.
Insha’ Allah this clears things up, and please feel free to ask any further questions you may have.
Wa assalaam alaikum wa rahmatullahi wa barakatuh.