Yes, the fuel pump go on the inside of the fuel tank. Is the fuel pump goes bad ?

Have an assistant to turn on the ignition switch, while you listen to the fuel pump running for 2 seconds from the uncap fuel tank filler. No noise, take the next step.
Try giving the bottom of the fuel tank a few whacks with a flat piece of wood or a rubber mallet while another tries to start the engine. You have a 50/50 shot at getting the pump going again and the vehicle starting. if it starts as a result of the whack then it confirms the bad fuel pump.
Here are the tips to access the fuel pump.
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Reducing the fuel pressure to zero is a very important step for correct removal of the electric fuel pump.
Disconnect the negative battery cable.
To access the fuel pump, the rear seat bottom must be removed.

If vehicle has no fuel pump access cover the fuel tank must be lowered or removed to gain access to the in-tank fuel pump.

Unplug the fuel pump harness connector.
Remove the fuel pump access cover.
Disconnect the fuel outlet and the return hoses. Use rags to catch any excess fuel.
Remove the fuel pump assembly-to-fuel tank bolts, and carefully lift the fuel pump assembly from the fuel tank. Discard the O-ring. Place a clean rag over the fuel tank opening to prevent dirt from entering the fuel tank.
To install:
Using a new O-ring, place the fuel pump assembly into the fuel tank.
Install the fuel pump assembly-to-fuel tank bolts and torque the bolts to 1.4-1.9 ft. lbs. (2.0-2.5 Nm).
Reconnect the fuel lines and the electrical connector.
Connect the negative battery cable, start engine and check for fuel leaks.
If all connections are secure, install the fuel pump access cover and the rear seat.

Keep in mind that the engine may take longer to start, since the fuel pump has to prime itself and pressurize the system. Be sure the battery is in good condition.

On some models, the "Check Engine Light" will stay on after installation is completed. The memory code in the control unit must be erased. To erase the code, disconnect the battery cable for 10 seconds then reconnect it after installation of fuel pump.

First step - have the check engine light or stored fault codes scanned - for free - at any local auto parts store; Advance Auto, Auto Zone, NAPA. Then, post a reply as 'add answer' for more assistance.

Possible Causes of Engine Hesitation or Stumble:

Dirty fuel injectors (cleaning the injectors often fixes this)
Dirty air filter (change filter)
Dirty / clogged fuel filter (change filter)
Bad MAP (manifold absolute pressure) sensor
Bad TPS (throttle position) sensor
Bad or dirty MAF (mass airflow) sensor
Low fuel pressure (leaky fuel pressure regulator or weak fuel pump)
Vacuum leaks (intake manifold, vacuum hoses, throttle body, EGR valve)
Bad gasoline (fuel contaminated with water or too much alcohol)

Sometimes, what feels like a hesitation is actually ignition misfire rather than lean misfire. The causes of ignition misfire may include:

Dirty or worn spark plugs
Bad plug wires
Weak ignition coil
Wet plug wires

First step - have the check engine light or stored fault codes scanned - for free - at any local auto parts store; Advance Auto, Auto Zone, NAPA. Then, post a reply as 'add answer' for more assistance.

Possible Causes of Engine Hesitation or Stumble:

Dirty fuel injectors (cleaning the injectors often fixes this)
Dirty air filter (change filter)
Dirty / clogged fuel filter (change filter)
Bad MAP (manifold absolute pressure) sensor
Bad TPS (throttle position) sensor
Bad or dirty MAF (mass airflow) sensor
Low fuel pressure (leaky fuel pressure regulator or weak fuel pump)
Vacuum leaks (intake manifold, vacuum hoses, throttle body, EGR valve)
Bad gasoline (fuel contaminated with water or too much alcohol)

Sometimes, what feels like a hesitation is actually ignition misfire rather than lean misfire. The causes of ignition misfire may include:

Dirty or worn spark plugs
Bad plug wires
Weak ignition coil
Wet plug wires

If the option is a used 2.4L engine - try these sources; www.risingsunengines.com, www.theautochannel.com, www.gearheadengines.com, www.woodfins.com, www.findapartnow.com, www.jdmenginescorp.com/engines/nissan - to list only a few.
These engines are plentiful and should be readily available via the used engine market and with a little internet surfing. Be sure to make the choice of an engine and source with the best warranty.

Did the repair shop or dealership state exactly why they believe a new engine is needed? What tests or diagnosis steps were done to determine this recommendation?

Yes, the a/c compressor (model Zexel #DKV14C) clutch is available as a separate item. Try these on-line parts sources for the clutch and any a/c compressor parts (such as: clutch coils or output shaft bearings); www.worldaire.com, www.ackits.com, www.polarbearinc.com - to list just a few sources.

Here is the compressor clutch service manual; http://www.cpsproducts.com/site/elements/download/PDFs

The Nissan part # for the clutch for the compressor is available from at least the Nissan dealer parts dept with part # 926650Z001, however, when you see the cost of just the clutch you may decide to replace the compressor with a complete remanufactured unit (many cases the compressor is new) for just a slight bit more. The price I see at Nissan parts is about $250 to $300 for just the clutch and I see complete reman compressors at various online sellers at $250 to $350.

The check engine light is located on the dash and stays on if the computerized engine control system detects an engine performance or emissions problem.

First step - have the stored fault codes scanned or check engine light - for free - at any local auto parts store; Advance Auto, Auto Zone, NAPA. Then, post a reply as 'add answer' for more assistance.

There are literally hundreds of possible fault codes to choose from - so the first step would be to read the fault code - 'check engine light' for the issue or condition.

Careucar prompt: that if the check engine light is on, you can get a car code reader to diagnose it, and you can quick to know what problems cause the light on.

You should be able to have the emission test as long as the check engine light is not on. If the dealer or repair shop has reset the memory to clear the codes - then you should be good to go.