Is this true?

In some case it is false, there are random changes in spelling, and normed spelling is a rather modern thing. But in most cases, especially since the orthography of French has been designed to reflect its etymology, different spellings stem from different origins, and thus likely different pronunciations.

Was main /mɛ̃/ pronounced /meɪn/ in Ancient French as in present-day English?

As far as I know: no. Latin for main is manus. Since then it has evolved roughly like this [manum] > [manu] (II) > [maɛnu (III) > [maɛn] (VII-VIII) > [maĩn] (X) > [mẽn] (Xe-XIII) > [mɛ̃n > [mɛ̃]

When did nasalisation happen and why?

Phonemic nasalisation in French is in most cases due to retrograde assimilation : e.g. vinum > vinu > vin [win] > [vin] > [vɛ̃] (I don’t know if it is the actual evolution.). The tables linked below give you the when: essentially between the XI and XIII century.

If you want more details, here is a summary of the nasalisation process in French with a detailed timeline of pronunciations. The site itself is a really good source for historical study of French, apart from that I use Noëlle Laborderie’s Précis de phonétique historique.

In some parts of France, people pronounce ‘an’ and ‘en’ in a slightly different way, yet the difference is perfectly audible. The same applies to ‘main’ and ‘vin’ or ‘brun’: the pronunciation is now similar in modern French, but people who still speak in an older fashion, or use local dialect, pronounce them differently.