Here is the translation of mOham AginEn inda vELaiyil. I enjoyed this padavarNam. Except for a tantalizing suggestion of SringAra, the varNam is lovely, and I particularly loved the 4th eTTugaDasvara sAhityam. I have made small corrections to the sAhityam as appropriate.pallavi
mOham AginEn inda vELaiyil mAran kaNaiyum pAyudE vagai ariyEn
I have become (AginEn) infatuated (mOham) at this (inda) time (vELaiyil), and I know not (ariyEn) the means (vagai) to escape even as the arrows (kaNaiyum) of manmatha (mAran) attack/torment/target (pAyudE)  me. anupallavi
yOgamigum ambalam tannil naTanamADum vAhan ennai maruva varuvAnO shollaDi
Tell me (SollaDi) my friend, will that handsome (vAhan) Lord who dances (naTanamADum) in (tannil) the propitious (yOgamigum) dance hall/temple (ambalam) in cidambaram ever come (varuvAnO) here to embrace (maruva)  me (ennai)? (ciTTasvara sAhitya)
kUDi irunda nALil kuLirnda candiran mODi sheyya anal vIsudE manam
vADi migavum nalam tEDudE unakku kOTi puNNiyamuNDu azhaittODi vADi
It looks as if the same moon (candiran) that was cool (kuLirnda) during the days (nALil) we were (irunda) together (kUDi) is now spewing out/pouring forth (vISudE) waves of heat (anal). My mind/heart (manam) is pining away in grief (vADi) and is searching (tEDudE) very heard (migavum) for love (nalam). You (unakku) will reap the benefits (uNDu) of countless (kOTi)  good deeds (puNNiyam) if you bring (azhaittu vADi) him to me post-haste (ODi) .caraNam
mAdE innum yOcanai EnaDi madi mayaNgudal vINaDi
Oh woman (mAdE), why (EnaDi) are you still (innum) lost in thoughts (yOcanai)? It is useless (vINaDi) to let your mind (ma(t)di) become confused/bewildered (mayaNgudal).eTTugaDasvara sAhityam 1
vAnOrgaL talaivanaik-kaNDAl pOdumaDi (mAdE innum...)
It is enough (pOdumaDi) if I were to merely meet/see (kaNDAl) the leader (talaivanai) of the celestials (vAnOrgaL), (Oh woman (mAdE), why (EnaDi) are you still (innum) lost in thoughts (yOcanai)? It is useless to let your mind become confused/bewildered).eTTugaDasvara sAhityam 2
nAnE tavangaLai purindEnE iniyum sahiyEnE tanittirundu tAnE enna sheiguvEn (mAdE innum"¦)
By myself (nAnE), I have undertaken (purindEnE) severe austerities (tavangaLai); I cannot bear (sahiyEnE) this continued separation anymore (iniyum); what (enna) can I do (SeiguvEn) if I exist/live (irundu) by myself (tAnE), all alone (tanittu)? (Oh woman (mAdE), why (EnaDi) are you still (innum) lost in thoughts (yOcanai)? It is useless to let your mind become confused/bewildered). eTTugaDasvara sAhityam 3
shonna mozhi tanai kanavilum maravEnE shollavum tiramaigaL illaiyaDi
kannam kuzhiya onru koDuttu maraindavan kanni endanai kaiviDuvAnODi (mAdE innum"¦)
Even in my dreams (kanavilum), I will not forget (maravEnE) the words (mozhi tanai) he spoke (Sonna), the promises he made; unfortunately, in this pitiable state of mine, I do not have (illaiyaDi) the capabilities/facilities (tiramaigaL) to say (Sollavum) them out loud for the world to hear . Oh friend, will that man who disappeared (maraindavan) after planting (koDuttu) one (onru)  so forcefully that it marked (kuzhiya) my cheek, now (kannam) abandon (kaiviDuvAnODi) me (endanai), a lovelorn maiden (kanni)? eTTugaDasvara sAhityam 4
sOmanaip-pOloru sundaran yAraDi jagattinil kUraDi
jAmattil shuDalaiyin sAmbalaip-pUsiyE sAdhuvaip-pOlat-tirivAnaDi
kAmanai erittavan yamanai udaittavan karuNai pozhiyum viDai vAhananaDi anda
amitan sheyalai nAn ariyEnaDi Adi cidambarattil amarndiruppAnaDi
Oh friend, tell (kUraDi) me who (yAraDi) is as handsome (oru sundaran) as (pOl) the moon (sOmanai) in this world (jagattinil). He roams (tirivAnaDi) around at night/midnight (jAmattil) like (pOla) an ascetic (sAdhuvai) with ashes (sAmbalai) from crematoria (SuDalaiyin) smeared (pUSiyE) all over his body. He is the one who burnt (erittavan) manmatha (kAmanai) and the one who kicked (udaittavan) yama (yamanai); he is the all merciful one who rides (vAhananaDi) a bull (viDai) showering (pozhiyum) compassion (karuNai) on us. I do not comprehend (ariyEnaDi) the acts (Seyalai) of that (anda) unmeasurable/unquantifiable (amitan) Lord who reclines (amarndiruppAnaDi) in the ancient (Adi) city of cidambaram (cidambarattil).
 pAyudE literally means 'springing' or 'flowing' with force
 maruva can also mean 'enjoy censored word union'
 kOTi/kODi - a crore
 ODi literally means 'run'
 I think the reference is to the fact that the nAyika is tongue-tied with unrequited love
 a kiss planted so forcefully, that it literally causes a hole/pit/crater (kuzhi) in the nAyika's cheek
Lakshman Sir, can you please check the lyrics of the Karaharapriya varnam in that link. Some of the lines seem wrong. For eg. the charanam is 'Maathey yaarukaagilum bhayamaa...idhu rahasiyamaa' but the link gives it different.
If the caraNa sAhityam is 'mAdE yArukkAgilum bhayamA, idu rahasiyamA
', it would translate to:
Oh woman (mAdE), as if I am afraid (bhayamA) of anyone (yArukkAgilum)! Is this (idu) a secret (rahasiyamA)?