Dear Upāsaka,
(1) Based on the dhammasanganī, the three types are earth (pathavi), fire (tejo), wind (vāyo). I mentioned this at the beginning of my answer.
"647. Katamaṃ taṃ rūpaṃ phoṭṭhabbāyatanaṃ? Pathavīdhātu tejodhātu vāyodhātu kakkhaḷaṃ mudukaṃ saṇhaṃ pharusaṃ sukhasamphassaṃ dukkhasamphassaṃ garukaṃ lahukaṃ, yaṃ phoṭṭhabbaṃ anidassanaṃ sappaṭighaṃ kāyena anidassanena sappaṭighena phusi vā phusati vā phusissati vā phuse vā phoṭṭhabbo peso phoṭṭhabbāyatanaṃ petaṃ phoṭṭhabbadhātu pesā – idaṃ taṃ rūpaṃ phoṭṭhabbāyatanaṃ.
Therefore, when counting the materiality, if the tactile object is considered, the three types of materiality (earth, fire, wind) has to be taken into account."
(2) This is the translation of the MNA
(Tipiṭaka Pāḷi Reader - Mūlapaṇṇāsa-aṭṭhakathā (pathamo bhāgo) - Para 78)
Tassattho – so anāgāmī evaṃ bhāvitabrahmavihāro etesaṃ brahmavihārānaṃ yato kutoci vuṭṭhāya te eva brahmavihāradhamme nāmavasena tesaṃ nissayaṃ hadayavatthuṃ vatthunissayāni bhūtānīti iminā nayena bhūtupādāyadhamme rūpavasena ca vavatthapetvā atthi idanti pajānāti, ettāvatānena dukkhasaccavavatthānaṃ kataṃ hoti. - The meaning of this is: that non-returner (anāgāmī), who has cultivated the divine abodes (brahmavihāra) in this way, having emerged from these divine abodes from any of them, determines (vavatthapeti) these divine abodes as “These states as mental phenomena (nāma), heart-base (hadayavatthu) as their (nāma of the divine abodes) base of support (vatthunissaya) and the four great elements are nissaya (dependants) of the dependants for the heart base ” in this manner, he determines (vavatthapeti) four great elements and derived materiality (bhūtupādāyadhamma) as materiality (rūpa). he knows (pajānāti) “There is this.” In this way, he has detemines the truth of suffering (dukkhasacca).
(3) In the two cases in the MNA and ANA which we are discussing here are using the verbatim which appears in Dhammasaṅgaṇīpāḷi itself. In the list in the MNA and ANA the list of the 12 gross matter (olārika-rūpa) is given as in classification of the bases.
(Tipiṭaka Pāḷi Reader - Mūlapaṇṇāsa-aṭṭhakathā (dutiyo bhāgo) - Para 347) - Gaṇanato na jānāti nāma, “Cakkhāyatanaṃ, sota-ghāna-jivhā-kāyāyatanaṃ, rūpa-sadda-gandha-rasa-phoṭṭhabbāyatanaṃ, itthindriyaṃ, purisindriyaṃ, jīvitindriyaṃ, kāyaviññatti, vacīviññatti, ākāsadhātu, āpodhātu, rūpassa lahutā, mudutā, kammaññatā, upacayo, santati, jaratā, rūpassa aniccatā, kabaḷīkāro āhāro”ti evaṃ pāḷiyaṃ āgatā pañcavīsati rūpakoṭṭhāsāti na jānāti.
In the Dhammasaṅīgaṇīpāḷi the terms āyatana (base), indriya (faculty), dhātu (element) are used for the materiality accordingly (based on the classifications) in the dyads etc. Eg:- Cakkhāyatanaṁ, Cakkhundriyaṁ, Cakkhudhātu (search for these words using Tipitaka app). The commentator has to use either of these words.
In the case of the tactile sense base, the three types of materiality are summarized in the Dhammasaṅīgaṇīpāḷi. The commentary uses the same summarisation. "(Tipiṭaka Pāḷi Reader - Dhammasaṅīgaṇīpāḷi - Para 647) 647. Katamaṃ taṃ rūpaṃ phoṭṭhabbāyatanaṃ? Pathavīdhātu tejodhātu vāyodhātu" .
(4) To distinguish it from the other five bases. The five bases (eye base, ear base, nose base, tongue base, body base) which serves as two sets of five types of consciousness (Eye-consciousness, -ear consciousness, nose-consciousness, tongue-consciousness, body-consciousness). These five bases which are similar in the application of the cognizing process, when distinguished from the heart base, it becomes easier to explain. The heart base functions as the base for 75 types of consciousness which are different in the application of the cognizing process.
(Tipiṭaka Pāḷi Reader - Mūlapaṇṇāsa-aṭṭhakathā (paṭhamo bhāgo) - Para98) Cakkhusamphasso…pe… kāyasamphassoti ettāvatā ca kusalākusalavipākā pañcavatthukā dasa samphassā vuttā honti. Manosamphassoti iminā sesā bāvīsati lokiyavipākamanasampayuttaphassā.
I think this different wording is intended for ease of reference for sarūpakathana (အရကောက်) and to remember the function of the paramattha dhamma easily. The terms like 'hasituppāda, sa ṅtīraṇa, dvipañcaviññāṇa/ pañcaviññāṇa, votthapana/voṭṭbana ’ doesn’t appear in the root. But in the atthasalinī, abhidhammattha-saṁgaha and in the sub-commenataries (please search for these words in the Tipiṭaka apps) them.
Eg:- For the pañcadvaravajjana citta
Root - (Tipiṭaka Pāḷi Reader - Dhammasaṅīgaṇīpāḷi - Para 566-567) - Dhammasaṅīgaṇīpāḷi - in the pāli the term “Kiriyā manodhātu” is used.
566. Katame dhammā abyākatā? Yasmiṃ samaye manodhātu uppannā hoti kiriyā neva kusalā nākusalā na ca kammavipākā upekkhāsahagatā rūpārammaṇā vā…pe… phoṭṭhabbārammaṇā vā yaṃ yaṃ vā panārabbha, tasmiṃ samaye phasso hoti, vedanā hoti, saññā hoti, cetanā hoti, cittaṃ hoti, vitakko hoti, vicāro hoti, upekkhā hoti, cittassekaggatā hoti, manindriyaṃ hoti, upekkhindriyaṃ hoti, jīvitindriyaṃ hoti; ye vā pana tasmiṃ samaye aññepi atthi paṭiccasamuppannā arūpino dhammā – ime dhammā abyākatā…pe….
Tasmiṃ kho pana samaye cattāro khandhā honti, dvāyatanāni honti, dve dhātuyo honti, tayo āhārā honti, tīṇindriyāni honti, eko phasso hoti…pe… ekā manodhātu hoti, ekaṃ dhammāyatanaṃ hoti, ekā dhammadhātu hoti; ye vā pana tasmiṃ samaye aññepi atthi paṭiccasamuppannā arūpino dhammā – ime dhammā abyākatā…pe….
567.katamo tasmiṃ samaye saṅkhārakkhandho hoti? Phasso cetanā vitakko vicāro cittassekaggatā jīvitindriyaṃ; ye vā pana tasmiṃ samaye aññepi atthi paṭiccasamuppannā arūpino dhammā ṭhapetvā vedanākkhandhaṃ ṭhapetvā saññākkhandhaṃ ṭhapetvā viññāṇakkhandhaṃ – ayaṃ tasmiṃ samaye saṅkhārakkhandho hoti…pe… ime dhammā abyākatā.- Kiriyā manodhātu
The abhidhammattha-saṁgaha uses the term "Upekkhāsahagata ṃ pañcadvārāvajjanacitta ṃ".
When a single phrase is used the reference becomes easier and the function of the consciousness can be easily understood i.e. the five-sense-door-adverting function. The term used in the pāli and the commentary here in “kiriyā manodhātu” which is deriving from the kusalattika.
(5) I will return to you the same question. Do you think that the Buddha had the intention to speak inaccurately and vaguely so that Commentaries could provide accurate, more helpful wording? Do you think that the Buddha’s wording is somehow no more as essential as the Commentarial wording? In my case the terms commentaries are using made the study easier for me. Maybe because I learned the Theravāda commentaries with an experienced teacher.