false etymologies and "False Freunde" for Tamil words ending in " -thiram" ?

[Chandrasekaran, Periannan]

This is related to Palaniappan's thread on Kumarila Bhatta's criticism of
false etymologies.
Since I have nothing to say about Kumarila Bhatta's criticism I am using a
separate thread.

I am addressing words in Tamil ending "-thiram".

Examples:
Tamil            Skt.                  popular sense of the (Sanskrit) words
man-thiram   man-thra     -  chant
chiththiram   chithra        -   picture
than-thiram   than-thra     -   trick
en-thiram      yan-thra      -  machine
in-thiran        indhra           -  God Ind(i)ra
chUththiram sUthram         - a terse verse (pardon the rhyme)

Then there are these exotic Tamil words:
used in Sangam era Tamil texts which made :

paithiram     -   country
    [pathirruppaththu:

   #1.
      19:18: "vAzthal IyA vaLanaRu paithiram"
      txln: "the countries  (of enemies) that offer no livelihood
   #2.

maathiram   -   1. sky 2.direction
 [malaipatu katAm:
     "malai patu katAm mAthiraththu iyampa"
    txln: "the sound of the elephants on the mountain echoing in all
directions]

I am under the impression that it is taken for granted in linguistic circles
also
that the Tamil words appearing here were derived from the Sanskrit words
listed to their right.  Tamil is assumed to have
to "softened" the "-thra" words into "-ththiram" by doubling the consonant
"th"
and always  inseritng the vowel "i".

I have already come across a few articles where the word "chiththiram" 's
etymology is given as
derived from the combination of Tamil roots "chil" + "thiRam".

Then I thought about the following famous chUththiram (or sUthram?) on
man-thiram
 in Tolkaappiyam [a few centuries BC] the classic Tamil grammar authored by
Tolkaappiyar,
student of Agaththiyar (or Agasthya).
"niRai mozi maan-thar aaNaiyiR kiLan-tha
 maRai mozi thaamE man-thiram enpa"
[poruL athikaaram: marapiyal???; I can quote the exact coordinates when I
get home].

This means:
"They (who have preceded me) say that the denying words that were born as
commands of
those great people who have stood firm in their words".
The key words here are: aaNai = command; maRai = maRu + ai = denial.
cf. aRai = aRu + ai.

Here "denying words" means that the words that deny or reject (maRu) the
wrong ways
and show the right way.
The word maRai is often mistaken to mean only "hide" or "hidden words".
But in Tolkaapiyam itself there are places where that word is used clearly
not to mean
"hidden" but "way" (or "treatise").:
"narampin maRai..."  - the way of the (musical) note = (roughly) music
treatise

This seems to be very different from the meanings associated with the
Sanskrit
word "man-thram"  which is closer to magic chant etc which is not  generally
thought to be in the sense of "great persons' commands".

In ThirumurukaaRRuppatai, the most distinguished book in Paththuppaattu
(the Ten Anthologies ) of classic Tamil Sangam,
there is a passage that uses the word "man-thiram":
"............................................orumukam
man-thira vithiyin marapuLi vazaa
an-thaNar vELvi OrkkummE...".

Note the phrase "man-thira vithiyin  marapu".
This does not seem to be clo