Kashmir was a secluded valley. So, once they got to rule there, there was no stopping them. There was large scale forced conversion. Half the Muslims in Kashmir carry Hindu surnames - Butt (Bhatta), Pandit, Kaul, Dar, etc.
From what I've observed, the priest will call out "archana?" before a puja. A family will approach him with fruits and a yellow ticket. I think I've only seen a tray or basket once... usually the fruits are brought in plastic shopping bags. I'll have to pay closer attention to what is done, when and how.
Yes, generally this is how its done in busier temples. He's just letting people know that the regular puja is over, and he's now available for archana. When archanas can be done varies from temple to temple. At one temple I went to (Salt Lake City Ganesha) the priest walked around and did archana for everyone present by walking around and getting everyone's name and nakshatra. (All for free of course) .
People in North India do their 'archanas' themselves. Lord understands all languages and dialects. One can do 'archana' ('ardas' for Sikhs) in Punjabi, Bengali or Gujarati.
Just one of many differences between styles. I love the diversity, and I don't see much point in highlighting all the differences. God is present at all Hindu temples.
Diversity is spice to life, Vinayaka. I too love it, and that is why I highlight it. Hinduism is a kaleidoscope view, it is like a multi-colored fractal.
Unfortunately not everyone can seer the big picture while still holding the narrowed view personally, for its strength. Many remain sectarian, ethnocentric, and behave as if there is only one language in India ... theirs. Most of its due to just not getting around much, and because of the nature of the world these days, that's changing rather quickly.