It’s called “rotor” and you can customize what on it under Voiceover settings

Go to iOS Settings > Accessibility > VoiceOver and there is a practice area where you can try out all the different gestures to hear what they all do. If you four-finger double-tap, that starts VoiceOver help which does the same thing. Going through that helps you learn, plus in iOS 13 you have a full list of all the VO gestures available to you that works as a perfect reference list plus is customizable.

What do you mean by APS? Do you mean Apps? I've found certain apps to be very accessible and iOS makes it much faster and more efficient to interact with certain things based on the overall speed of doing it with a desktop screen reader. Twitterific, BaconReader, Lyft, Kik, Blindsquare, Be My Eyes, Aira, native Apple apps like Messages, Mail, Voice Memos, etc., so many apps are built accessibly and VoiceOver works well with them, and since there are less design pitfalls with native apps versus websites, the native mobile app experience is just faster overall depending on what you are doing.

The rotor options will change based on what you are focused on. If you go to Settings > Accessibility > VoiceOver > Rotor, you'll get an editable list of everything you can access in the rotor. I have that set up with only the things I need including text selection and braille screen input.

When you land on a text field, turning the rotor to the left once or twice will bring you to the Edit options. When you are on Edit, swipe vertically to toggle between the action you want to perform; select, select all, paste, look something up in the dictionary, etc. once you've found the action, such as paste, just double-tap the screen with a single finger to activate that action. iOS will then paste whatever you have copied into the text field. You can practice text editing in the Notes app, just create a new note, focus on the note text field, and try typing, selecting, copying, cutting, pasting, etc until you feel comfy with it.

For overall speed, I highly recommend learning braille and using braille screen input. When you are on a text field, the braille screen input option will show up in the rotor, and a 6-key keyboard will show up on the screen. I hold my phone in landscape mode with the screen facing away from my body. That gives my hands and fingers the perfect position to curl around the phone and tap the screen with 6 fingers, typing with braille characters that get interpreted into text. It's how I'm typing this response right now and being able to use contracted grade 2 braille drastically speeds up typing and interaction.

As for apps, just go about it understanding that VoiceOver is putting a cursor on the screen and left and right swipes move that cursor up and down the interface respectively, element by element. A good app will have all buttons, links, text fields, etc. labeled and clearly understandable, while a bad app will have nothing labeled, cursor traps where you suddenly can't move the cursor, all manner of accessibility pitfalls. There is no recourse there apart from contacting the developers and explaining what is going on and hopefully they listen and fix it. I've had good success with that so far, just takes a little persistence.

I'm not sure on what you mean by, "pop-directional format"
I'm sorry.