1. False. Many newer devices utilizing the A/B partition layout don't have a dedicated `recovery` partition. See [landing page for Google Pixel](https://twrp.me/google/googlepixel.html) for a full explanation.
 2. True. Certain devices have exploits that allow recovery on locked bootloaders - this kind of recovery is often referred to as "Safestrap". Do note "exploits" - most devices don't have such discovered.
 3. True - partition size is usually the same as `boot`. On my Xiaomi Mi Mix 2, both are 67108864 bytes, i.e. 64MB.
 4. True - recovery can be considered a minimal OS by itself (with complete display, input, file management subsystems). If you want to start a regular OS by booting into `recovery`, just flash a regular boot image (one that usually goes into `boot`) to `recovery`.