I addressed Chinese earlier and ignis_glaciesque expanded.
As for Japanese, there are a lot more contractions than shortened names and nouns, especially in dialects. See:
そっちんワープロじゃ、使えんっちゅうこっちゃないけど Socchi’n waapuro ja, tsukaen 'chuu kotcha nai kedo
(It’s not that it can’t be used with the word processor over there.)
Versus:
そちらのワードプロセッサでは、使えないということはないけれども Sochira no waado-purosessa de wa, tsukaenai to iu koto wa nai keredomo
That’s an extreme example but contractions like 'chatta for te-shimatta, socchi for sochira or ja for de wa are a fundamental part of the language.
I should also point out that, at least in such dialects as I’m familiar with, “have to”, “going to”, “want to”, etc., only reduce where “to” serves to introduce a (possibly elided) infinitival phrase. Thus, at least in my dialect, you can say “I’m gonna leave soon” but not *“I’m gonna the store”. This is fairly similar to the sorts of things which happen with more “standard” contractions; e.g., “I can’t remember” vs. *“I can’t only speak Russian, but read it as well” or “If I’d studied more, I would’ve done better” vs. *“If I were rich, I would’ve a lot of money”.
To be complete, there are also spoken-only contractions, such as 'Worcester" (or a town down South, written “Maryville” but pronounced “Murrville” by those who live there).
I suppose written-only contractions would be called abbreviations.
Spoken Bengali and Hindi use some contractions. They can be written if you want to. (Anything that can be spoken can be written in the Indian writing systems.) I don’t have an extensive knowledge of written Bengali or Hindi, but I assume that “modern” literature that uses vernacular language would use written forms of the contractions.
Nope! They’ll sometimes drop the final “o” on the nouns, as in this example from the Esperanto hymn: * “Al la mond’ eterne militanta ĝi promesas sanktan harmonion.”*
Seems Thai does have at least two contractons, as I was reminded today. Dichan, one of the words for “I,” is often shortened to chan. And prachanan, which means “therefore,” is occasionally chanan.