al-mu'tamad المعتمد in Arabic basically means established and approved.
So when speaking about a ruling in a madhab and say this is the mu'tamad in this madhab then we mean despite all other opinions in the madhab the chosen view, which almost all scholars of the madhab would pronounce in a fatwa is this selected opinion.
In the following I'll be quoting and translating from this fatwa from islamqa #194735 (Note that I've linked some key words to an Arabic-English dictionary and tried to show off when I used the keyword mu'tamad in my translation).
كل مذهب من المذاهب الأربعة المعتمدة عند أهل السنة والجماعة , قد مر بعدة أطوار , يمكن حصرها في الأطوار التالية : النشوء والتكوين , ثم التوسع والنمو , ثم الانتشار , ثم الاستقرار , وهذا الطور الأخير هو ما يطلق عليه " تحرير المذهب " , ومعنى تحرير المذهب " نَخْل مصنفات أئمته وشيوخه ، وبيان ما هو موافق لقول صاحب المذهب وأصوله ، حتى يصح أن ينسب إليه ، ويتميز عن غيره من الوجوه والاجتهادات التي لا يصح أن تنسب إلى صاحب المذهب ، وتُعتبر مذهباً له " انتهى من مقدمة الدكتور عبد العظيم الديب " لنهاية المطلب في دراية المذهب " (المقدمة / 153) بتصرف.
- - - (My own translation take it with the necessary care) - - -
Each of the four madhabs of ahl-asunna wal-Jama'a has passed a couple of phases, which we can limit in four phases:
the birth and building up النشوء والتكوين
the expansion and growth التوسع والنمو
the diffusion الانتشار
the stabilization and fixedness الاستقرار.
This last phase is also referred to as tahrir al-madhab تحرير المذهب, this means taking all the works of the Imams and great scholars of the madhab and separate the wheat from the chaff by showing off which among this views belongs to the Imam and his osol (sources), to make clear whether one could refer to it as his view, and refer to the ijtihad of others as their single opinion which are not of his own, but can be reffered to as his madhab . (outtakes from the introduction of Dr. Abdual'adhim a-Dyb on "Nihayat al-Matlab fi dirayat al-Madhab").
In the shafi'i madhab those great scholars who had the most influence on the stabilization of the madhab are Imam an-Nawawi النووي (died 631 a.H.) and ar-Rifa'i الرافعي (died 623 a.H.) , who in the shafi'i madhab are called a-sheikhan (the two sheikhs), so anything which is now considered a ruling in the madhab is based on their statements, compilation and research with the following meaning:
فأصبحا عمدة من جاء بعدهما من فقهاء الشافعية , فينتهي الاجتهاد إلى رأيهما , وتكون الفتوى على اختياراتهما ما اتفقا , فإن اختلفا فالمعتمد ما اختاره النووي , وإن وجد للرافعي ترجيح ولم يوجد للنووي فهو المذهب المعتمد ,
So their opinions became that which is counted or relied on as "The madhab" for those who came after this two among the shafi'i's, so Ijtihad is -practically- finalized at their opinions, so fatwa can only be based on their choice, at what they agreed upon, if they had a disagreement than the chosen madhab (al-mu'tamad) is what an-Nawawi has chosen, but if ar-Rifa'i had a weighting which an-Nawawi didn't have then it (the view of the first) would be the chosen madhab (al-mu'tamad).
Some later Shafi'is even went so far to say if a statement of an-Nawawi was contradicting Imam a-Shafi'i then the madhab view would be the one of an-Nawawi! Also note that of course later scholars validated and checked this opinions and maybe corrected a view here and their.
(This thread -in Arabic- discusses technical terms of the shafi'i madhab, a lot of that is on the topic of when trying to refer an opinion to scholars or references of the madhab)
Imam al-Ghazali's quote
I found the quote in a fatwa referring it Ihya' 'ulum ad-Dyn (which I can confirm) this is the statement
وإذا اجتمع قلتان من ماء نجس طهر ولا يعود نجساً بالتفريق
هذا هو مذهب الشافعي رضي الله عنه ؛ وكنت أود أن يكون مذهبه كمذهب مالك رضي الله عنه ، في أن الماء وإن قل : لا ينجس إلا بالتغير ؛ إذ الحاجة ماسة إليه ، ومثار الوسواس : اشتراط القلتين ؛ ولأجله شق على الناس ذلك ، وهو لعمري سبب المشقة ، ويعرفه من يجربه ويتأمله
If an amount of impure water, equal to two pitchers (qullatayn or two Qullah), should gather in one place, that water would become pure if mixed [with a larger quantity of pure water] This is the position of a-Shafi'i. I hoped however, that his position would be like that of Malik who held that water, no matter how meagre its amount might become, would not be rendered impure (najis) except through change [in taste, colour or odor], because the need for it is great and to lay down the condition of two pitchers would simply provoke suspicion (waswas) and fear. It has therefore become very difficult to observe this rule and, upon life, it is difficult; those who would try and examine it would find that out for themselves.
(Translation is basically taken from the translation of Nabih Amin Faris book of "Mysteries of Purity" Page 15-with some explanatory Additions of mine- which is available here)
Imam al-Ghazali is referring here to the hadith of al-qullatayn (two Qullah or pitchers) which you may find in sunan books like ibn Majah, an-Nasa'i, abu Dawod and Jami' at-Tirmidhi and the hadiths narrated by abu Said al-Khudri (sunan abi Dawod, sunan an-Nasa'i, Jami' at-Tirmidhi, sunan abi Dawod with details), ibn 'Abbas (sunan an-Nasa'i) Jabir (sunan ibn Majah) and abu Ummamah al-Bahili (sunan ibn Majah) which are the basis of the opposite view.
Ijtihad
I'll try to find something more than what I could present you at the moment -which is basically my understanding- :
"the decision whether one would declare a new madhab or not (doing Ijtihad al-Mutlaq) is up to the scholar and his understanding and interpretation of verses such as 16:43, 7:33 and especially 6:159 ..." (ASSUMPTION)
