T7 triggered data acquisiton

Hello  i am learning Lab jack .i got to know that T7 has a  triggered data scanning mode.What is the minimum pulse width required for triggering T7 for starting data acquisition ?

Sounds like you are asking about the feature where stream start is triggered by a digital logic transition.  The spec for minimum high or low time is 50 ns:

https://labjack.com/support/datasheets/t7/appendix-a-2

Only stream mode can be used for triggered acquisition?

Yes, but there are other similar things you can do not using stream mode:

A.  You can have software poll a digital input and when you see the desired change grab analog input readings.

B.  You could have a Lua script do the same as A above, except the script could poll the digital input faster.

C.  If your pulse is very quick and you worry that polling a digital input would miss it, you could use a counter instead.  Then software or script just polls the counter to see if it has incremented.

data sheet tells us  that max sample rate  depends on resolution index 0 or 1. What is meant by resolution index ?

ResolutionIndex is a parameter you can control that affects how the device does its analog to digital conversions.  When you increase ResolutionIndex the noise generally decreases and sample time generally increases.

"Sample => A reading from one channel/address".  How many addresses make one channel?

1 address is the same as 1 channel.  The terms can usually be used interchangeably.