The huruf muqatiaat means separate, so why all qaris do ikhfa and idgham when reciting them?

Question
Assalamualaikum,
My question is that if the huruf muqatiaat means separate,so why all qaris do ikhfa and idgham when reciting them?. jazakallahu khair.

Answer
Wa alaikum assalaam wa rahmatullahi wa barakatuh,
What is meant by separate letters (referring to the separate letters that begin some of the surahs), is that the letters are pronounced as the name of the letter, not as a word.  At the same time, we apply the tajweed rules to the saakin letters at the end of the name of each individual letter. 
For example, in the first aayah of surah al-Baqarah, Allah ta'aalaa said:
We don't pronounce this as alam or alim, instead we read it as the name of each of  letters, alif, laam, meem, and we apply the tajweed rules since is considered to be a single word, even though the letters are pronounced by their names. 

For more details, please see:
http://www.abouttajweed.com/the-mudood-the-lengthenings-/the-mudood-lengthenings-part-9.html