How to hunt respected and honest organisation ,
Start with alibaba.com, they are a large b2b website listing many Chinese manufacturers, importers, and exporters. I did a quick search and found dozens of Chinese companies offering phosphoric acid there.
How to negotiate the price to lower and other duty for importing the products ,
Usually if you buy in large quantities you can get discounts, additionally, if you accept shipping terms that do not put all the risk on them they can price accordingly.
As for duty that is a tax from your country and usually not negotiable. The Chinese manufacturer has no control over Indian import taxes.
How to believe if any company asking for advance payment .
Sometimes you can order smaller samples and establish a working relationship with less risk, but you are asking a very generic business question. You could fly over to meet them like some people do (when I imported from China and Malaysia our company flew out to speak to them in person).
But if you want you can also negotiate shipping terms more favorable to you (e.g. see here
for examples of common ones).
In my experience, once they trust you a bit more they will be willing to change payment terms, so often you pay in advance the first orders and in the future they give you payment terms like net 30 or somesuch.