There is a .godot file, but idk if that’s it. Should the name literally be project.godot file? I couldn’t find anything named project.godot, although there is a project.binary file.
Yes there usually is one and its called “project.godot”. I think it only contains project settings, so i guess you can create a new one or copy one from another project
You can’t open exported projects in the Godot editor. You can only run them. The exporting process distills the game files into a compressed form that cannot be edited.
How are you transfering files? If you have a USB drive you can copy the entire folder onto it, then copy the folder onto your other computer. If you must use the internet then you may have to Zip the project folder, on windows you can right click the folder and select “send to > compressed file”
I would encourage using a version control system like git or ark to both share between computers and keep regular back ups of your project