This is a movie song...as far as the lyrics go, I do not see how the first part (about Siva) fits into the second part (about bharatanATyam)
ADum aruL jOti aruLvAi nI yennai
pADum pAvai yen mEl pArA mukham yEn (ADum aruL jOti...)
Oh benevolent/merciful (aruL) effulgence (jOti) that dances (ADum), you (nI) please bless (aruLvAi) me (yennai). Why (yEn) are you neglecting (pArAmukham/pArAmugam) [1] me (yen mEl) [2], this singing (pADum) damsel (pAvai)?
mAnum mazhuvum Endi...
malar pAdam tUkki
Adiyum antamum tAnumAi
tadIngiNatOm enRu (ADum aruL jOti...)
(Oh benevolent effulgence that dances) to mnemonic syllables that go (enRu) 'tadIngiNatOm' while becoming (tAnumAi) both the beginning (Adiyum) and the end (antamum) [3], as you hold/bear (Endi) a deer (mAnum) and a battle-axe (mazhuvum), raising (tUkkiyour flower (malar)-like foot (pAdam) (please bless me)!
bhAvam rAgam tALam sErnda kalai
bhAvam rAgam tALam sErnda bharata kalai
inda pAril uLLOr enRum pOTRum kalai
EDil yEdum unDO idarku iNai nam
nADum koNDADum paNpADum kalai
This art form (kalai) of bharatanATyam (bharata) is the confluence (sErnda) of expression/emotion (bhAvam), melody (rAgam), and rhythm (tALam) [4]. It is an art form (kalai) that will forever (enRum) be praised (pOTRum) by the residents (uLLOr) of this earth (pAril). Is (uNDO) there any (Edum) equal (iNai) to this (idarku) (art form) anywhere in this world (EDil)? It is an art form (kalai) celebrated (koNDADum) by our (nam) country/land (nADum) as well as our culture (paNpADum) [5].
FOOTNOTES
[1] pArAmukham can also mean turning one's face away
[2] yen mEl literally means on (mEl) me (yen)
[3] this is a fairly complex concept in a movie song - I think this can refer to two things - a) the fact that Siva's tANDavam is both the dance of creation (Adi) and destruction (antam) AND b) the fact that Siva has no beginning and end
[4] a reference to the new (at the time this movie was made) christening of sadir as bharatanATyam based on the bhAvam rAgam tALam concept
[5] paNpADum can also be split as paN pADum - in which case the last line would be translated as ' It is an art form (kalai) celebrated (koNDADum) by our (nam) country/land (nADum) and sung about (pADum) in our music (paN)'