Why doesn't Watney, who is desperate to communicate after he is stranded on Mars that he is, in fact, still alive, arrange rocks, equipment, etc., to make some sort of signal that could be read from overhead? After all, he knows that a Mars orbiter could be taking photos of his site, and it's an ancient tradition to write "S-O-S" or "H-E-L-P" when stranded on a desert island. Why leave it to chance for NASA to interpret changes at the site to show that he's still alive?
After the airlock blows, Watney re-seals the entrance using a flimsy tarp fastened by duct tape. Yet, as a subsequent scene in the movie shows, this tarp is buffeted by high winds--and given the (knowingly inaccurately) powerful sandstorm that blew an antenna that impaled him and trapped him at the first place, Watney had to have feared that even a tiny object could have caused a catastrophic puncture. Why didn't he double-layer the protection, insted of leaving himself to a rapid depressurization?
Even given advances in technology and remote control, why wasn't an astronaut left aboard the Hermes when it's in Martian orbit? After all, there are plenty of things that could go wrong aboard such a vast spacecraft, not to mention the potential need to maneuver the Hermes to rendezvous with the MAV. Does it really make sense to leave it completely deserted, as opposed to leaving at least one astronaut aboard (as was done during Apollo, with the Command Module pilot in lunar orbit while the other two crew members went to the surface aboard the LEM and then returned)?
As mentioned before in this forum, book has some inaccurate descriptions about how it was supposed to be on Mars. Please consider that while you're reading or watching The Martian.
Answer to your 1st Question
Basically, the crew thought Mark was dead. And Mark assumed they thought he was dead too. So he presumed there was no possibility of NASA checking up on him via satellites. Mark way busy trying to survive.
Also, it was mentioned in the book, the satellite images are shared publicly. They didn't want to share a dead astronaut's last resting place with the entire human race through social media.
Answer to your 2nd Question
The author of the book Andy Weir briefly explained during one of his interviews that his description of Mars athmosphere is not scientifically correct. First of all, Mars athmosphere is not thick enough to produce a storm that strong. Secondly, if we presume Mars athmosphere was thick enough to produce a storm like that, that duct tape sealed gate wouldn't hold (Please check the link above). So, you are correct.
Answer to your 3rd Question
It was mentioned both in the book and the movie, HERMES does not have enough fuel to stop at Mars orbit and wait until they do their thing to save Watney and go back to Earth. If they went back to save Mark and waddle around Mars a bit and then save Mark somehow, they would die during their way back to Earth (presumably).
That's why they used The Rich Purnell Maneuver. NASA explains that the RPM was the best way to use planetery gravity to gain velocity in order to maintain their very little left supplies (Also they needed supplies, so... you can watch the video I put in the link).