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: