1.Historicaly For how long has there been offical inflation rates  
published in USA?

Hello again bluekat

"Various indexes have been devised to measure different aspects of
inflation. Two commonly used indexes are the Consumer Price Index
(CPI) and the US Implicit Price Deflator for Personal Consumption
(IPD). The CPI measures inflation as experienced by consumers in their
day-to-day living expenses.... There are a number of other indexes of
price changes other than the CPI and IPD: the Producer Price Index
(PPI) measures inflation at earlier stages of the production and
marketing process; the Employment Cost Index (ECI) measures it in the
labor market; the Bureau of Labor Statistics' International Price
Program measures it for imports and exports; and the Gross Domestic
Product Deflator (GDP-Deflator) measures combine the experience with
inflation of governments (Federal, State and local), businesses, and
consumers. Finally, there are specialized measures, such as measures
of interest rates and measures of consumers' and business executives'
inflation expectations."
Information from "Topics in Economics: Inflation" State of Washington
web site
http://www.ofm.wa.gov/economy/econtopics/inflation.htm 

The CPI is the most commonly used measure, and has been calculated
each year since 1913 by the Bureau of Labor Statistics.
The Bureau has an inflation calculator, which lets you compare the
buying power of a specific sum of dollars between any two years from
1913-present.
You can access this at the Bureau's web site: http://stats.bls.gov/
There is a link to the calculator on the top left of the home page.  

The Bureau supplies a full set of historical data from 1913 to the
present at
ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt
The reference base for these figures is the period 1982-1984: "BLS
sets the average index level (representing the average price
level)--for the 36-month period covering the years 1982, 1983, and
1984--equal to 100. The Bureau measures changes in relation to that
figure. An index of 110, for example, means there has been a
10-percent increase in price since the reference period; similarly an
index of 90 means a 10-percent decrease. Movements of the index from
one date to another can be expressed as changes in index points
(simply, the difference between index levels), but it is more useful
to express the movements as percent changes. This is because index
points are affected by the level of the index in relation to its base
period, while percent changes are not."
From the CPI FAQ 
http://stats.bls.gov/cpi/cpifaq.htm 

search strategy: searching on "official inflation rate" combined with
USA led me to a several pages stating that the official rate is
published by the Bureau of Labor Statistics.  I then searched on
"Bureau of Labor Statistics"

thankyou, good work