How can I connect fuel level sender to a gauge and micro-controller simultaneously
The fuel gauge and sender form a simple voltage divider network, with the gauge resistance fixed, and the sender being proportional to fuel level. As the sender resistance changes the current through the gauge changes and the needle moves. You can calculate the sender resistance in situ by just measuring the voltage across the sender directly. I can't remember the exact numbers, but the gauges are usually 200 ohms or something, so the voltage range is between 1-6 volts (for a 12V supply).

Also note that changes in the battery voltage will affect the measurement, so you might want to measure this as well if you need good accuracy (also note most factory fitted fuel senders are horribly inaccurate).