Can hydrogen gas be an alternative fuel source for a gas turbine engine? I want to do research for an alternative fuel source for a commercial aircraft that will reduce the cost for flights.

Will the hydrogen gas be ignited in the combustion chamber and produce enough thrust to power the aircraft for flying? As for the problem that people had stated before for storing the gasses in a high pressure gas tank, can an increase in the aircraft weight be reduced by replacing the tank with usage of a hydrogen generator instead of a whole bulky tank that will weigh more?

By using a generator which converts water into hydrogen gas, we can just use water as our main fuel source which is more cost efficient?

In a flame of pure hydrogen gas, burning in air, the hydrogen (H2) reacts with oxygen (O2) to form water (H2O) and releases energy. If carried out in atmospheric air instead of pure oxygen, as is usually the case, hydrogen combustion may yield small amounts of nitrogen oxides, along with the water vapor.
Yes, and it has been demonstrated 30 years ago on the Tupolev 155. This is/was a hydrogen-powered version of the Russian Tu-154B tri-jet. Only one has been built and has since been retired after demonstrating the use of liquid hydrogen in 5 experimental flights. In total, the Tu-155 performed about 100 flights with several fuels, among them hydrogen and liquefied natural gas.



Tu-155 (top), cut-out (center) and layout (bottom). Source: https://www.aviaru.net/pr/?id=11633

Hydrogen is actually better for a jet engine: It is gaseous at normal temperature, so there is no delay for the evaporation step to happen as there is for liquid fuels before mixing and combustion can start. Also, hydrogen burns in a wide variety of mixing ratios with oxygen, so flame-outs are much less likely, making a smaller combustion chamber possible.

The downsides, of course, are storage and the small molecular size of hydrogen. It is very hard to contain, and it needs big volumes to store a given amount of chemical energy. Pressurized storage at 200 bars holds only 18 kg/m³ or 45 times less than kerosene. With 142 MJ/kg, hydrogen holds three times as much chemical energy than kerosene, but then the volumetric efficiency of kerosene is still a factor of 13.3 better.

Cryogenic storage swaps pressure for low temperature: Below 33 K and above 13 bar, hydrogen becomes a liquid and storage density increases to 30 kg/m³. Still, cryogenic hydrogen storage needs 4 times the volume of the same amount of energy stored as kerosene, plus the isolation and the energy to cool it down and compress it.