* FreeRTOS is a good place to start, but there are many, both OS and commercial. Most are similar in scope and application. Larger systems may also use Linux or Android, but that's further away from what you're looking for.
* Atmel, Arm, PIC, ESP8266/ESP32 are probably the strongest current players. Procs like the Cortex M series are popular on the Arm side, Atmels are what the non-Arm-based Arduinos run, and the ESPs exploded on to the scene as a dirt-cheap way to get WiFi.
* shrug Arduinos, ESPs, and RPis. There are a million other boards like the Tiny series. Adafruit has the Feather series which I like quite a bit, and the Circuit Express which is an interesting proposition, but has a Python layer, which you may or may not want. Note that almost all of these boards can be developed for in different ways: the Arduino "IDE", command-line Arduino or bare-metal, JavaScript, etc.
* That you'd just have to search for--the embedded landscape is huge because almost everything has a processor in it now at some level. If it's a company that makes a physical product that does anything other than sit there, there's a processor in it. (More or less.)