If you change the aspect ratio of saved images to 1:1, the lowest available resolution option for the EOS Rebel SL2/200D is 1600x1600 pixels. How to change the camera's aspect ratio is covered in the EOS Rebel SL2/200D User Manual.
How can I enter a custom image size straight from the camera (to skip having to resize every time)
You can't unless you write your own firmware for the camera.
If the above is not possible, can I go to a lower resolution than S2? I noticed that in other tutorials online, there is the S3 resolution option:
The EOS Rebel SL2/200D does not offer an S3 option. Some other Canon EOS cameras offer an S3 option. For example, the EOS 5Ds with a 50 MP sensor: set to 1:1 aspect ratio it has a 640 x 640 pixel S3 option. The video you linked is for the EOS Rebel T3i/600D. When set to 4:3 aspect ratio (it does not offer a 1:1 aspect ratio), it offers an S3 resolution of 640x480 pixels.
last but not least: is there a way to custom enter the image name for each image?
Not in the way you desire. Folder and file names on camera memory cards are governed by the Design rule for Camera File system standard. Images must be stored in a folder named 'DCIM' and in subfolders that also must meet certain naming conventions.
DCIM is short for Digital Camera IMages and is part of the industry standard outlined by the Design rule for Camera File system. This standard was adopted as the de facto standard for storing digital image and sound files in memory devices by the digital camera industry to insure interoperability from one brand to the next.
Design rule for Camera File system (DCF) is a JEITA specification (number CP-3461) which defines a file system for digital cameras, including the directory structure, file naming method, character set, file format, and metadata format. It is currently the de facto industry standard for digital still cameras. The file format of DCF conforms to the Exif specification, but the DCF specification also allows use of any other file formats.
The default form of an image file name is IMG_0001.
- It must be 8 characters in length.
- The first four characters may use A-Z, 0-9, and _ (except for the first character which can not be an _ - This is because when you are working in the AdobeRGB color space instead of sRGB, the first digit will be replaced with an underscore _).
- The last four characters can only be numbers between 0-9. They are assigned by the camera in sequence as each image (or video) is successively taken. When the last four characters reach '9999' the camera automatically creates a new folder (also assigned in sequence based on the naming convention requirements) and begins again with image '0001' (it skips '0000').
There are certain ways to instruct the camera to create new folder and reset file numbers when certain conditions are reached. Whatever options the EOS Rebel SL2/200D offers with regard to file names are covered in the EOS Rebel SL2/200D User Manual.
Some Canon cameras allow modifying the standard 'IMG_' prefix to a user selected four character string that complies with the above requirements. I doubt the entry level Rebel SL2/200D does, but you can alway check the EOS Rebel SL2/200D User Manual. Models that do allow this customization include instructions on how to do it in the Manual.