All three sentences are grammatically correct, but they're not all the same. In the first one,
A hotel is there in the middle of the Thor desert in India.
the speaker/writer isn't in the middle of the Thor desert. And although it's grammatically correct, it's probably not the optimal way of using existential "there".
In the second one,
There is a hotel in the middle of the Thor desert in India.
the speaker/writer may or may not be in the middle of the Thor desert. It is, however, the normal way of using existential "there": at the beginning of the sentence.
In the third one,
There is a hotel here in the middle of the Thor desert in India.
the speaker/writer is in the middle of the Thor desert in India, and adding the here emphasizes that point. If that's what you want to focus on -- your presence there in the middle of that desert at the time of writing or speaking -- that's fine.
In the fourth one,
There is a hotel situated in the middle of the Thor desert in India.
all you've done is inserted a pleonasm, a verbosity, an unnecessary word. Hotels don't fly or crawl or trot through the desert the way birds, snakes, and camels do. Therefore, they are always situated/located wherever they are. That the hotel is situated in the middle of the Thor desert in India is already clearly stated by the locative preposition "in" and the phrase "in the middle of..."
MW onlnine gives this example sentence: "They decided to situate the new office building near the airport." My personal opinion is that this is a poor word choice. It should most likely be "build", but because the direct object is "building", someone thought "situate" was better for the sound; it could have been "erect" or "construct".
Macmillan online gives these examples: "This modern three star hotel is situated close to the city center." and "The Business Library is situated on the ground floor."
All these sentences are grammatical, and the structure is used, but that doesn't mean that it's optimal or good style. If you delete the word situated, the sentence means the same thing and sounds better because it doesn't have that unnecessary word.