How O'Brien highlights the difference between the "real world" and the "safe world".

Throughout the story O'Brien draws a line between the "real world" and the "safe world". The real world being Jimmy's world, the war, where men are die everyday, where the people live under extreme conditions, where life itself becomes a burden sometimes and needs to be carried by the men. The safe world being Martha's world, where they care about literature, have no danger to life, enjoy with friends, and live life to fulfill their dreams.
O'Brien compares the life of the people in both the worlds and shows the significant different. This is done mainly through the comparison of the life of Jimmy Cross and that of Martha. Even though the story is mainly about Jimmy's realization, it can be seen that a difference is established by the end of the story. Jimmy Cross even talks about the difference. "...she belonged elsewhere. He would shut down the daydreams. This was not Mount Sebastian, it was another world, where there were no pretty poems or midterm exams, a place where men died because of carelessness or gross stupidity"(O'Brien 383). This sentence is one of examples given by other to outline the two separate worlds.
Jimmy Cross lives in a world of pistols, machine guns, grenades, tanks, jet fighters, etc. and Martha lived in a world of poetry, shopping, beaches, parties, movies, etc.
The moments where Jimmy Cross escapes from reality are the moments where the differences can be noticed and these moments usually came after a description of their weapons was given. It can be noticed that by putting the story in such a format the author is actually trying to establish somewhat of a boundary between the two worlds. This pattern is followed till the second last page of the story where the story changes to a somewhat different format to describe the ending of the story.

In Gryphon, describe three ways Baxter intertwines the conventional and unconventional and for what purpose this interplay is used.

Baxter intertwines the conventional and unconventional in very significant ways.
There is the conventional teacher Mr. Hibler and then there is the unconventional teacher Ms. Ferenczi. Baxter does a great job of outlining the differences between them. Mr. Hibler teaches according to the curriculum and does not stray from it whereas Ms. Ferenczi does not like teaching the usual stuff and goes out of the lesson plan to tell the kids what she thinks about different topics. For example, when the students tell her that Mr. Hibler always started with the pledge she just ignores it and goes dirctly to the book to start studying. Here we can see that she is being unconventional by clearly defying Mr. Hibler's usual routine. She never teaches the students by the lesson plan but rather comes up with material created by herself, this shows that Ms. Ferenczi is an example of how Baxter intertwines the conventional and the unconventional.
Another example is when she declines the offer to go to the teacher's lounge to eat with the other teachers. Even though every teacher goes there to eat she refuses and says that she preferred eating with the students. Here it can be seen that she is again being unconventional by separating herself from the other teachers. This example may not be as significant but small examples like these show how Baxter excels at showcasing the personality the of a person by minute details.
Another example is when she comes to teach the students a second time. She does not even look at the lesson plan and starts telling the fortune of the students. This example is the most significant one and can be seen by even those people who are not looking for evidence to show the conventional and unconventional. Firstly, a classroom is not a place for superstitious things like fortune-telling. Secondly, the teacher should have taught according to the lesson plan. This shows that she likes to teach by her own ways and not be conventional. But Baxter balances it out with the last paragraph where the kids taught the lesson properly hence intertwining the conventional and the unconventional.

In a story about the Das Family and their taxi driver while on vacation, do you believe Jhumpa Lahiri constructed a hopeful story? Or otherwise?

I believe that the ending of the story is hopeful and that Jhumpa Lahiri was actually trying to create a hopeful ending. It may be argued that it is a depressing story with a sad ending but there are several instances in the story which will make the reader think that it is indeed a hopeful story.
One of the most notable instances is the ending; Mrs. Das shows through her actions that she does care for her family, that she loves Bobby even though he is not Raj's son and was never intended to be born. This act of affection from Mrs. Das towards her family is a proof that it is a hopeful story. At the start of the story she is confined to herself, she does not pay much attention to any of her kids, has her glasses on at all times as if hiding guilt under them. But at the end she gets out of the car without putting on her glasses, this is a big step toward getting more involved and attached. Also she is worried about Bobby; all of this show that she is trying to change and that she is becoming a person who cares a lot about her family. It is seen that towards the end she is willing to help Bobby. The fact that she wants to change to become a better human being is an indication that it is a hopeful story.
The monkeys who are usually known to be wild and uncontrollable become silent and calm towards the end. This is an unusual behavior and therefore cannot be overlooked. Perhaps they are portraying the feelings of the Das family at any given time. At first they are loud and frustrating like the feelings of guilt inside Mrs. Das but later on they are silent and calm probably like Mrs. Das who has started to realize that her pain is really guilt and therefore her pain has decreased.