What is Prana according to Buddhism? According to Buddhism, does flora contain prana? Is this a cosmic energy that is set in earth, nature? Do organisms contain that energy?
In Theravada Buddhism, we call it pāṇa, which is just the Pali cognate of the Sanskrit prāṇa. The word itself just means breath, though it has connotations that come from Hinduism, regarding the concepts of life essence, soul, energy, etc. The PED gives some idea of how it is used in Buddhism:

Pāṇa [fr. pa+an, cp. Vedic prāṇa breath of life; P. apāna, etc.] living being, life, creature D iii.48, 63, 133 S i.209, 224; v.43, 227, 441 (mahā -- samudde); A i.161 ii.73, 176, 192; Sn 117, 247, 394, 704; Dh 246; DA i.69 161; KhA 26; ThA 253; PvA 9, 28, 35; VvA 72 DhA ii.19. -- pl. also pāṇāni, e. g. Sn 117; Dh 270. &lt;-&gt; Bdhgh's defn of pāṇa is &quot;pāṇanatāya pāṇā; assāsapassās' āyatta -- vuttitāyā ti attho&quot; Vism 310.
 -- âtipāta destruction of life, murder Vin i.83 (in &quot;dasa sikkhāpadāni,&quot; see also sīla), 85, 193; D iii.68, 70, 149 182, 235; M i.361; iii.23; Sn 242; It 63; J iii.181 Pug 39 sq.; Nett 27; VbhA 383 (var. degrees of murder) DhA ii.19; iii.355; DA i.69; PvA 27.  -- âtipātin one who takes the life of a living being, destroying life D iii.82; M iii.22; S ii.167; It 92; DhA ii.19.  -- upeta possessed or endowed with life, alive [cp. BSk. prāṇopeta Divy 72, 462 etc.] S i.173; Sn 157; DA i.236  -- ghāta slaying life, killing, murder DA i.69;  -- ghātin   âtipātin DhA ii.19.  -- bhu a living being J iv.494  -- bhūta=˚bhu M iii.5; A ii.210; iii.92; iv.249 sq. J iv.498.  -- vadha=âtipāta DA i.69.  -- sama equal to or as dear as life J ii.343; Dpvs xi.26; DhA i.5.  -- hara taking away life, destructive M i.10=iii.97; S iv.206 A ii.116, 143, 153; iii.163.

In Theravada Buddhism this is as far as the concept goes, and it is only conceptual; there is no sense of an actual &quot;spirit&quot; or &quot;energy&quot; living inside of the body that can be called pāṇa; it is only the concept of a living, breathing being that is described as pāṇa.  As the Visuddhimagga explains:

Breathing things (pāṇa): so called because of their state of breathing (pāṇanatā); the meaning is, because their existence depends on in-breaths and out-breaths.
Vism. IX.54 (Nyanamoli, trans)

In Tibetan Buddhism, though, there seems to be more of a recognition of the existence of an energy flowing through the body, a &quot;psychic wind&quot; (Tibetan: rLung), so to speak:

Some of the different usages of the term lung include:

the psychic winds (sanskrit: prana) that travel in the internal channels, or nadi (Sanskrit) of the subtle body and are manipulated in certain Vajrayana yoga practices.
specifically the five psychic winds that are a manifestation of the Mahabhuta. These five are the lifeforce that animate the bodymind (Sanskrit: namarupa) of all sentient beings and are key to certain tantric Buddhist and Bon sadhanas and Traditional Tibetan medicine.
to the vayu and prana of ayurvedic medicine.
as a component of the term for a type of prayer flag, named after the allegorical Wind Horse (Tibet: lung ta).
a type of tantric buddhist empowerment that involves the transference of spiritual power from master to augment or refine that of the disciple through the recitation of scripture or song. This oracular transmission received aurally defines Mantrayana and Ngagpa traditions and provides them with their nomenclature.
the &quot;reading transmission&quot; of sutrayana texts, in which the entirety of the text is read aloud from teacher to student.

-- Wikipedia, Lung (Tibetan Buddhism)

Tenzin Wangyal Rinpoche devotes an entire section of his book &quot;The Tibetan Yogas of Dream and Sleep&quot; to the topic of prana.
In answer to your auxiliary questions, it again depends somewhat on which tradition you follow, but I think the consensus is that only sentient beings share the quality of prana, however it is understood.