Starving Angels

Hunger woke them up once again. They though they would have been used to it by now, but they weren't.

( note 1  become is probably better than get in prose; note 2 it would probably be a good idea to define the main actors. In other words, who are the people? Young schoolchildren? Nursery infants? etc - note 3  would have become used to ....is set in the past of the past (pluperfect or past perfect) and implies they still weren't used to it. Therefore, grammatically you need the past simple finite  weren't in the clause "but they weren't. Keep the four main time zones  in mind:  past perfect - past - present - future note 4 I have made "Hunger" the subject of the sentence to give it more thematic power in the flow of your discourse.   )

Trying to cheer themselves up, they checked the school's free lunch menu and pictured the delicious meal they would be having  that day.

( they are not eating yet, so the action of eating will actually happen in the future. However, the main time frame for the narrative is in the past simple hence they would be eating.  if you were in the present time frame, you might say something " I can just imagine what we are going to be eating later/will be eating later)   

These little angels can be found in any corner of the world. They manage to be content with what they have and cherish everything offered just like what they've promised God to do. ( The clause I have crossed out doesn't make any logical sense, even if you make the grammatical adjustment just as promised God they would do/or would have done. Perhaps you could try to reconnect it in some way) 

But is seems that their prayers aren't going to be answered this time 'round/ haven't been answers this time 'round.  

But it seems that their prayers aren't answered this time. ( Note 1 You have changed time frame, which as a literary device is quite OK, but you have to adjust everything else, too. Now you are in the present time, which gives dramatic effect, so you need a future tense for the main proposal in the clause.

Soon, there won't be any more such free lunches for them anymore because of an impetuous budget cut by the government.

note 1 It is very easy to confuse the adverb anymore with the nominal elements any more.  2. the term impetuous doesn't really collocate very well here. In short impetuous  implies hast, speed, rush, hurry, etc.   Perhaps terms like insensitive, uncaring etc  might be more suitable. You could even omit the adjective and let the reader draw their own conclusions, which are quite obvious.

Starving Angels

This is very sad, and you're right these situations can be found all over the world.  Thank you for writing about it.  (And you have written well!)