Addressing
How does the lunar module of Apollo 11 reached an orbit speed of 1600 meter/second in order to rejoin the CSM (Command/Service Module)?
This table from APOLLO EXPERIENCE REPORT -
MISSION PLANNING FOR LUNAR MODULE
DESCENT AND ASCENT by my former colleague Floyd Bennett shows the delta-v requirements for the Apollo 11 ascent to be 6055.7 feet per second and that the Lunar Module Ascent Engine had plenty of performance to make it with the propellant load on board.

For detailed information on the ascent propulsion system, please consult the Experience Report here.
Addressing
Where are the Oxygen & Fuel tanks of the module? is there a schema / specification of the lunar module we can look?

From the Air and Space Museum website.