Your question is tagged "Abhidhamma" and "Pāḷi Canon", so I am going to limit my answer to the Theravāda perspective. I am only going to answer the first part of the question. Please leave me a comment if you want me to answer the other parts of the question (I want to make sure that we are on the same wavelength before proceeding).
Here is an entry as part of Nyanatiloka’s Buddhist Dictionary:
paramattha (-sacca, -vacana, -desanā): 'truth (or term, exposition) that is true in the highest (or ultimate) sense', as contrasted with the 'conventional truth' (vohāra-sacca), which is also called 'commonly accepted truth' (sammuti-sacca; in Skr: samvrti-satya). The Buddha, in explaining his doctrine, sometimes used conventional language and sometimes the philosophical mode of expression which is in accordance with undeluded insight into reality. In that ultimate sense, existence is a mere process of physical and mental phenomena within which, or beyond which, no real ego-entity nor any abiding substance can ever be found. Thus, whenever the Suttas speak of man, woman or person, or of the rebirth of a being, this must not be taken as being valid in the ultimate sense, but as a mere conventional mode of speech (vohāra-vacana).
It is one of the main characteristics of the Abhidhamma Piṭaka, in distinction from most of the Sutta Piṭaka, that it does not employ conventional language, but deals only with ultimates, or realities in the highest sense (paramattha-dhammā). But also in the Sutta Piṭaka there are many expositions in terms of ultimate language (paramattha-desanā), namely, wherever these texts deal with the groups (khandha), elements (dhātu) or sense-bases (āyatana), and their components; and wherever the 3 characteristics (ti-lakkhaṇa, q.v.) are applied. The majority of Sutta texts, however, use the conventional language, as appropriate in a practical or ethical context, because it “would not be right to say that 'the groups' (khandha) feel shame, etc.”
It should be noted, however, that also statements of the Buddha couched in conventional language, are called 'truth' (vohāra-sacca), being correct on their own level, which does not contradict the fact that such statements ultimately refer to impermanent and impersonal processes.
The two truths - ultimate and conventional - appear in that form only in the commentaries, but are implied in a Sutta-distinction of 'explicit (or direct) meaning' (nītattha, q.v.) and 'implicit meaning (to be inferred)' (neyyattha). Further, the Buddha repeatedly mentioned his reservations when using conventional speech, e.g. in D. 9: "These are merely names, expressions, turns of speech, designations in common use in the world, which the Perfect Qne (Tathāgata) uses without misapprehending them." See also S. I. 25.
The term paramattha, in the sense here used, occurs in the first para. of the Kathāvatthu, a work of the Abhidhamma Piṭaka (s. Guide, p. 62). (App: vohāra).
The commentarial discussions on these truths (Com. to D. 9 and M. 5) have not yet been translated in full. On these see K N. Jayatilleke, Early Buddhist Theory of Knowledge (London, 1963), pp. 361ff.
In Mahāyana, the Mādhyamika school has given a prominent place to the teaching of the two truths.
In DN 9, you will find the quote, "[names] are the world's designations, the world's expressions, the world's ways of speaking, the world's descriptions, with which the Tathāgata expresses himself but without grasping to them."
Regarding this verse, Thanissaro Bhikkhu makes the comment:
The Commentary takes this is as the Buddha's affirmation of the idea — which in later centuries became current in all schools of Buddhism — that he spoke truth on two levels: conventional and ultimate. In context, though, the Buddha seems to be referring merely to the fact that he has adopted the linguistic usages of his interlocutors simply for the sake of discussion, and that they should not be interpreted out of context.
Regarding this verse, Maurice Walshe makes the comment:
An important reference to the two truths referred in [the Dīgha Nikāya commentary] as 'conventional speech' (sammuti-kathā) and 'ultimately true speech' (paramattha-kathā). It is important to be aware of the level of truth at which any statements are made. In the [Majjhimma commentary to MN 5], the following verse is quoted (source unknown), 'Two truths the Buddha, best of all who speak, declared: conventional and ultimate – no third can be. Terms agreed are true by usage of the world; words of ultimate significance are true in terms of dhammas. Thus the Lord, a Teacher, he who is skilled in this world’s speech can use it, and not lie.'
Here is my personal conjecture (this is my own assumption, I have not seen this anywhere else, so take it with a grain of salt). According to the Wikipedia page on “Atomism”, the idea of breaking things into “ultimate realities” arose in India around the time of the Buddha and was adopted by some of the Buddha’s “competitors” such as the Jains, Ājīvikas (followers of Makkhali Gosala) and Carvaka schools. My assumption is that Buddhist had to defend themselves in debates against these “competitors” and felt that the Buddha’s overlapping analysis of aggregates / bases / elements was not “robust” enough to counter the detailed ontological arguments put forth by the “competition”.
As a response, each Buddhist school created their own set of "ultimate realities". Just to give an indication of the differences between schools: the Theravāda school has 1 citta (arising in 89 or 121 combinations, Mental States), 52 cetasika, 28 rūpa and 1 unconditioned element. The Sarvāstivāda school had 1 citta, 60 cetasika, 11 rūpa and 3 unconditioned elements. The Sautrāntika school had 6 citta, 29 cetasika, 8 rūpa and 1 unconditioned element. The Yogācāra school had 8 citta, 75 cetasika, 11 rūpa and 6 unconditioned elements. Each of these schools used the same set of Suttas, but analyzed them in a different way, according to their own doctrines.
Second part of the question
In AN 4.94, the Buddha defined samatha as a process of steadying, settling, unifying and composing (saṇṭhapetabbaṁ, sannisādetabbaṁ, ekodi kātabbaṁ, samādahātabban) the mind. When discussing samatha, the Suttas do not specify an object or a type of object (concept or ultimate reality). Samatha is a process, irrespective of the object. The result of samatha is internal tranquility. Of course, the commentaries focus on the object of samatha.
The same sutta describes vipassanā as distinct seeing of things through higher wisdom. Vipassanā is described as viewing saṅkhārā, investigating saṅkhārā and distinctly seeing saṅkhārā. The object of vipassanā is saṅkhārā. In this context, saṅkhārā can be interpreted as being the three characteristics (anicca, dukkha, anattā). The result of vipassanā is the insight knowledges.
Concepts do not possess the three characteristics and are therefore not valid objects of vipassanā meditation. On the other hand, citta, cetasika and rūpa do possess the three characteristics and are therefore valid objects of vipassanā meditation.
So it is important to know the difference between conventional realities and ultimate realities to understand the teachings. It is also important to only use ultimate realities as the object of vipassanā meditation.
