Remarkable that Jews and Muslims are leaders in food safety. Did not realize this
until the question was asked. In my travels with my work, I have always appreciated Halal, Kosher and anything blessed by whomever. In my mind, it means food is the source of life and should be appreciated and honored.

Generally, observant Ashkenazic Jews do not eat any rice for Passover while Sephardic Jews do. It has to do with the rulings of the ancient rabbis.

Yes, you can find kosher for passover certification on many products. Some products do not need this and others do. Yes, it can get very complicated depending upon how orthodox, also whether Ashkenazi or Sephardic. A friend of mine from Chabad always asks his rabbi when in doubt.

If the rice is unenriched or organic, it should be, according to my friend. Processed rice may use a starch base that may not be kosher for passover.

It really depends on "how Kosher"..and how strict. Corn is not kosher (for passover) but Kosher at other times.
Kosher for passover is different than just Kosher.

In fact this is good time of year to check for cococola at Jewish markets to find Coke, made without corn syrup.

As for rice, I really don't know, but the rule of thumb is that grains stored near wheat are not passover blessed and they shouldn't be in contact with water for more than 18 mins. (I'd be interested in knowing how they came up with that number..instead of 20 mins).

http://muslimconsumergroup.com/qa/index.php/551/enriched-jasmine-enriched-without-symbol-vitamins-sourced says "All vitamins enrichment in all flour, rice and corn are Halal and they are not made from animal sources." And I have seen jasmine rice with the kosher symbol