Is possible to convert it from FWD to AWD?

Yes. This is possible on most all vehicles but I don't show this being an option for your vehicle. That means this is extremely more complicated. This means that you have to now source the parts that will fit your vehicle and fabricate the parts needed to hold them in place. In other words, because this was not an option, I would not try it. If an AWD option was available for this vehicle then it would be just a matter of getting the parts and they would bolt up but again, I would not try this.

It would be far easier to purchase a vehicle that is AWD and sell this one as is.

I attached the options below showing that FWD is the only option. Let me know if you have other questions on this. Thanks

The JDM and Euro versions of the Galant are very different and only share the same name. The chassis is different between an AWD and FWD and has the points on it to install the rear differential and AWD suspension and the mounting underneath to mount the drive shaft. Plus the fuel system is different as the AWD driveshaft runs through a notch in the fuel tank that you don't have. Then you would need to change the transmission and engine as the transmission with AWD option won't bolt to the US engine.
Then once you get the mechanical system in you would need to rewire much of the car to make the new pieces work as the BCM/PCM are also different.
So while it could be done, the only part of your current car that you would be keeping would be most of the body shell. If you are in any of the places that require emission or safety inspections those will be another hurdle as the car was never offered as an AWD option that year, so now it's going to be a custom build and has to meet current standards.

Try eliminating the belt itself, remove it and start the engine, no squeak = Look at each item the belt drives and see if the pulley or tensioner turns freely. Examine the belt itself and make sure it is in good shape. If you still have the squeak with the belt off, there is a problem internally with the engine.

Just remove the front accessory belt and start it. If the loud squeal is gone you shut off the engine and start hunting on the accessories. If the squeal is still there then you have a worse problem, the description sounds like a metal on metal issue, but it could easily be something like a stuck alternator or idler and what you hear is the belt dragging on it.
How about this, take a video of it and post it. That alone would help. Then shoot a close up video showing the drive belt and as many of the items it drives like the idlers, alternator, power steering and such with the engine off, that may also help.

That is belt squeal, Easy test, take a spray bottle or just some water and with it running spray some on the belt in the wheel well between the AC and the crank pulley. The bearing in the pulley on them can cause a lot of drag when they start to fail. The other main screamer could be the alternator. Use the water and see where using it changes the sound. You say it goes away after a while so that sort of makes me think it's alternator, If you let it stop, then turn on the lights and heater blower to high does it start again? Another trick to spot a binding item, take a piece of chalk or a marker and with the engine off draw a line across each of the pulleys. Then have someone start it while you watch them.

The last thing is that it could simply be the belt is loose. Both of those have manual tensioning instead of automatic, so as a belt wears and stretches it will need to be tightened. To do that the images below show the locations of the tensioner bolts. You loosen the pivots on the alternator and tighten the bolt to put more tension on the belt. To measure if it's correct, simply push down on the center area between the two pulleys, it should move about one quarter inch. Tighten the pivots back down, then start it and see if the noise is gone. To adjust the other belt you go to the pulley between the PS pump and the AC, loosen the center bolt on the tensioner and use the indicated bolt to tighten that belt to about the same amount. Try it again, if it's quiet you're done.

Yes, that is on the alternator, the other adjuster is between the AC and power steering.