Question

where and when was the first british factory estabilishe?

Answer 1

All your questions (and one that was not a question) can be answered by reading and rereading your text and the following information, too.

http://www.bbc.co.uk/history/british/empire_seapower/east_india_01.shtml

http://www.sscnet.ucla.edu/southasia/History/British/BrIndia.html

http://www.indianchild.com/history_of_india.htm

and others --
http://www.google.com/search?hl=en&source=hp&biw=1173&bih=582&q=history+of+britain+in+india&aq=f&aqi=g1&aql=&oq=