What varieties of English that pronounce the word "rat" as [r æ?]? What do we call this phonetic process?

This process is called glottalization . Glottalization is found quite widely in English pronunciation , especially that of younger speakers. This glottalised pronunciation , in which a glottal stop occurs just before p , t , k , is only found in certain contexts , and foreign learners usually find the rules too difficult to learn.
Glottalization التهميز glottal stop الهمزة glottalised sound الصوت المهموز
التهميز تجده في كلمة إذا
Give two examples in which sounds get assimilated to each other.

In connected speech , sounds belonging to one word can cause changes in sounds belonging to adjacent (neighboring) words . When a phoneme is realized differently as a result of being near some other phoneme belonging to a neighboring word we call this an instance of assimilation . For example that person ,where the first word ends with the consonant t and the second word begins with p, is pronounced
δæp pз:sn.

Is the velarized /ℓ / distinct from the 'clear' /ℓ / in English? Are they two different phonemes? Is that also applicable to the Arabic language? Illustrate with examples.
As a matter of fact, both the verlazied / l / and the clear / l / belong to the same phoneme which is / l / . We can say that the velarized / l / and the light one are two different realizations or two different pronunciations of the same phoneme. This is also applicable to the Arabic language . his is very clear in the word Allah . The / l / is sometime pronounced verbalized مفخمة and other times it pronounced in a clear way مرققة

What is meant by pulmonic egressive airstream mechanism?

The muscles in the chest that we use for breathing produce the flow of air needed for almost all speech sounds. This airstream goes out of the lungs. That is why it is called pulmonic and egressive. The air stream is pushed out of the lungs into the windpipe upward into the larynx. When it reaches the larynx, it goes through either the oral cavity (the mouth) or the nasal cavity ( nose). If the soft palate (velum) is raised against the pharyngeal wall, the airflow will not be able to escape through the nose.