I've been told that the accent falls on the third syllable in the name Devanagari and that the other two A's are almost completely elided. So it sounds more like dayv-NA-gri, only three syllables. Is this approximately correct in most Indian languages, or perhaps in Sanskrit pronunciation?
Many of the other writing systems of southern and eastern Asia are derivations from Devanagari, including Punjabi and even languages of other families, such as Mongolic and Austro-Asiatic.
The technical term for writing systems like Devanagari is an abugida rather than an alphabet. In an alphabet, in most cases each letter represents only a single phoneme. (English and French really push that limit but most of the European languages have more precise sound-to-letter correspondence.) In an abugida, each letter represents a combination of one consonant and (optionally in some languages) one vowel. Unlike the Japanese, Cherokee and other syllabaries, in which each symbol is unrelated to any other, an abugida has a paradigm for logically combining symbolic elements that consistently represent a specific consonant or vowel, so learning and interpreting text is not as difficult as Japanese hiragana and katakana syllables.
The other widespread type of phonetic writing is the abjad. An abjad only has symbols for consonants; vowels are not recorded. Hebrew and Arabic are the most well-known abjads, but most of the Afro-Asiatic languages use them. The reason for this explains the unique nature of the abjad. In the Afro-Asiatic language family (which includes the Semitic as well as the Berber, Chadic, Cushitic, Egyptian and Omotic branches) vowels are not phonemic. You can write a word using only the consonants, and everyone will know which one you mean, unlike English where bad bud bade bed bid bead bawd and bode are all different words. Abjads have been modified for use in non-Afroasiatic languages, such as Yiddish, in which vowels matter. As I understand it, even in Modern Arabic some of the symbols have been co-opted to stand for vowels, as has been done with the Hebrew abjad to turn it into a Yiddish alphabet.
Call it abiguda if you are more comfortable. In our language, Devanagari is a Lipi.
लिपि
Each swar aka consonant is a syllable. Please do not make the mistake of extrapolating roman script rules to Devanagari. This has five sounds, modified by what you call vowel extension.
देवनागरी DEVANAAGARI.
d is pitman thee. e following it is replaced by a symbol. a after v is for your convinience and is is silent [but mind you there are no silent letters in Hindi]. aa after n is replaced by a symbol, a after g is for you only, i after r is replaced by a symbol. A consonant can be used stand alone, like v here, no modifier symbol is needed.
you wrote gri. No, it is gari, though a after is silent for you, does not exist for me as it does not combine with g to nodify the sounf of g.
You have names for letters ie g is gee, spoken like jee. In devanagari, each symbol is stand alone, and is known by its symbolic sound.
Once more. Each language is nearly unique, and so are there scripts. One theory for all is just not possible.
Grammar is the heart and engine of Sanskrit and Hindi language. Urdu uses Hindi grammatical rules. Come on, even Persian grammar is heavily influenced by Sanskrit grammar. Other India languages have grammar derived from Sanskrit. Even Pali follows Sanskrit in grammar.
Sanskrit has a unique feature. It has no dialects, while other Indian languages have. Even Hindi and have scores of them, changing every 10 miles. Lols. My mother is from a village just 9 miles away from mine. There beebee means sister, but here we use it for mother. But in general, beebee means respectful address for a woman, and includes mother, sister, daughter or any other woman, even a stranger BUT NOT wife.
Why not have a look at Pitman? Can say pitman jay? Then Dev is theeplus ay as in jay. Piman has 40+ symbols, schema like Devanagari.
PS: Have you heard? A significant break through ib deciphering the Indus script? It is by an Indian crypto analyst, who gave a go bye to the pre-existing notions and drew heavily from Indian languages. Language turns out to a Sanskrit like one!!