They are normally called Mordvin(ic) languages.
I know: the variant
Mordovian, which does exist too, just appears somewhat more euphonic to me.
Not impossible, but, sadly, absolutely not provable either.
Agree. Yet when two contiguous languages develop some feature that separates them from all their neighbors, this raises suspicions that this is not totally casual. I don't draw any solid conclusions, just point to that in both cases when a Slavic idiom has postposed definite articles, some neighbor language of a different group possesses it as well, which may be suggestive or not.
I also must stress that East Slavs have come into proper contact with the modern Mordvinic peoples rather late; although the chronicles mention a lot of Finnic tribes, Mordva is first mentioned only under 1103, if I am not mistaken. Even though Mordvinic languages do have several loanwords from Old Russian, it's incomparable with the amount of later (XVI-XX сс.) influences. I'd think about Muroma in the first place, who have left Mordvinic toponymics as well and were assimilated rather early (mentioned as a political entity in retrospective only, and its archaeological culture disappears around the XI century already). However, that creates a problem of the rather large time interval between the assimilation of Muroma and the first appearance of the postpositive definite markers in written sources. Plus Muroma was a rather small tribal union compared to, say, Merya - who, however, apparently were Mari-speaking.
I am not aware of any positive evidence about the languages of Muroma and Merya and about the time of their final disappearance. In all probability they were Finnic, but that's virtually all we know for sure. I am also not aware of any written sources reflecting the north-eastern East Slavic speech of the first half of the second millennium. As an example that this is important: the very particular north Krivichian dialect casually recovered from excavated birch bark manuscripts left only faint traces in the official texts of Novgorod and Pskov origin.
Speculating in the framework of the above hypothesis, we may conjecture that the definite declension arose in the area of Russian/Volgaic contacts (perhaps Slavic being the source of this phenomenon) and spread to Mordovian from the then-spoken related languages of the upper Volga.
Generally, I struggle to see how definiteness might be an area phenomenon, if that particular area seemingly did NOT represent a tight group of interconnected languages by the postulated moment. It looks more like a loan, either from a substrate or from a superstrate. The first hypothesis rises some questions mentioned above. The second is also far from being perfect, taking into account that in Mordvinic languages the definiteness represents a fully developed, finished cathegory, unlike in the North Russian dialects we know.
It is not quite developed since it is formed somewhat differently in both Mordovian languages and in different case forms (the definite particle gets attached sometimes before the ending, sometimes after it: cp. the Erzyan Elative Singular
kudo-sto-ntʲ vs. Plural
kudo-t-nʲe-ste: it is inserted between the Plural marker -t- and the Elative marker -stO), and in Mokshan only three cases (Nom. Gen. and Dat.) have separate definite declension. Overall, being agglutinating languages, Mordovian have less structural limitations for introducing new elements to the paradigm: they already had the personal declension (my/thy/his/our etc.), and the definite particle just replaced in the Singular the personal marker: compare
kudo-sto-ntʲ "from the house" and
kudo-sto-n "from my house(s)",
kudo-sto-t "from your house(s)",
kudo-sto-nzo "from his house(s)" etc. That was much more difficult in the inflectional Russian grammar (though it did happen some centuries before, in the compound adjectives:
nova-jego, novu-jemu etc.).
Although Mongolian influence is extremely unlikely for sure

, this argument is hardly relevant. If you loan some syntactical cathegory like definiteness, it's absolutely not necessary to express it the same way as in the source language; more likely, you'll find some means in your own language.
Practice shows that grammatical calques are often as literal as possible. The brain is lazy. Compare for example the spoken Slovene
en and
ta, which calque the German
ein and
der.
Which doesn't help us a lot. In fact, if the reduplication in тътъ didn't happen, we very well could have a pronoun "от" by now.
Don't get your argument.
Столот is the direct phonetic outcome of
столътъ like
днесь is of
дьньсь. Other Slavic languages either vocalize
ъ (Slovene
ta), or add
-jь (Belarusian, Ukrainian and Bulgarian
той), or do both (Serbo-Croatian
taj), or add
-enъ (West Slavic). None has
**ot.