itch.io

Step 9) there is no "Sync" option. I've looked everywhere and clicked on random things to find it. I do NOT have that option.

That sync option should appear as a bar between the file’s tab and the contents, like so:

If you do not see that bar, then it may mean that Android Studio failed to sync the project the first time, when you opened it, and it may be related to this other problem:

Step 2) When I click on "Build" tab, I don't get a "Build" nor "Build APK" option. I have no clue how I did it before. I clicked stuff there and it happened. But none of them worked for me in any kind of way.

This should be called Build Bundle(s) / APK(s) now, but if you do not see that option it means that Android Studio had problems reading the Gradle project and will not show that option until you have fixed the issues.

Android Studio / IntelliJ is a bit taciturn when there are Gradle problem, and it seems that everything is OK until you manually open the Build tool window and see lots of errors described there:

You can open the “Build” tool window in the Edit→Tool Windows→Build menu. Sometimes the error messages a bit obtuse, but it should give you enough clues to advance and at least sync the project the first time.

Step 10) This wasn't in the video, but there is no way for me to change my apk name. In fact, there is no "Manifests" folder. 

Maybe RPG Maker no longer creates the manifests folder, but there must be an AndroidManifest.xml somewhere.  You can locate files within Android Studio with Ctrl+Shift+N or the Navigate→File… menu.

To  itch you must upload the .apk inside a zip[…]

There is no need to zip the APK, because an APK is already a kind of ZIP file, therefore you only add an extra, useless step for the player to install the game into their devices.