Electronic – Is it possible to use SIM900 GPIO to control relays without using external MCU

Without the BGA pads, that's just a QFN package with 1 mm pitch. Yes, you can solder that with a hot air station.

The way I usually do this is to use a soldering iron to put a bead of solder on all the pads. Then smear paste flux over everything and position the chip over the pads as accurately as you can. A mag light is handy for this. The paste flux acts like goo to hold the chip in place.

Now heat with hot air at around 700°F. Make sure you have reasonable air flow, but no so much that the force of the air can move things around. For a package this large, you need to have one of those nozzles that has a long and thin vent for each side of the package. Be careful to hold the hot air wand steady and centered over the package. It may take 5-10 seconds, but you should see the solder melt. Make sure it is melted all around on all four sides, give it maybe another 2 seconds like that to be sure, and remove the air.

It is important that the solder on all pads be molten at the same time. Molten solder has significant surface tension. In the beginning, some of the pads will be molten, which pulls the chip down against the remaining pads harder. This is how the process deals with the inevitable mismatch of a higher solder beads than others. Once the solder on all pads is melted, they all pull together to line up the chip nicely with all its pads.

1. As it comes to datasheets they are indeed divided. "Reference manual" is complex descriptions of how to do things, configuration and detailed considerations about the whole MCU. "Datasheet" is on the other hand only a brief description of MCU features, pinouts, packages etc. There is also very helpful document for every STM32 line (F1,2...7) "Getting started with STM32F7xxxx MCU hardware development" which provides you with many informations if case you would like to design a custom board. In comparison to AVRs, registers descriptions are sometimes put a bit aside from main description of particular chapter.

2. STM32CubeMX is not a library, just a useful program from ST, which enables you to set pinouts, its configurations, set systems clocks etc and then, at the end, generate a code and the whole project. The project can be generated specially for Eclipse (System Workbench for STM32) in which you just import this project and you're ready to go. The new library is HAL ("hardware abstraction layer") and try to use it. That's the new thing and sometimes it's hard to find examples on the Internet but don't teach your students outdated technologies. HAL is convenient to use and has documentation, so I think it's better choice.

3. Which library? Anyway it shouldn't be a problem to google them, I think.

4. Even if you would like to use only one OS (like Windows), Eclipse (AC6 = System workbench for STM32) is - I think - the best option. There is for example Keil's uVision 5 - but that's really terrible IDE - it lacks most of features IDE should offer (refractoring, click-and-search, proper error checking, finding references and many, many more). So, all in all, the Eclipse is pretty much the only reasonable choice for IDE for STM32.