Greetings Elena2,
The green squares are focus boxes that the camera will show when auto focusing, but there would be an issue if they do not move when pressing the shutter button halfway down to focus on a specific subject within the frame.
The first thing I would suggest to do is to clean the front of the lens element with a dry microfiber cloth while the camera is powered on since debris on the lens may affect the focusing system of the camera.
For the other issues, let's reset the camera to see if this helps resolve these problems. You may follow the steps on page 165 of the user guide for the PowerShot G5 X camera for resetting the camera.
https://gdlp01.c-wss.com/gds/3/0300020273/01/psg5x-cu-en.pdf
In case the camera is still not functioning correctly, then we recommend on sending it to our facility for service.
Canon U.S.A., Inc. has created a new online repair portal that allows you to set up service in a few simple steps. The repair portal gives you the ability to set up service for multiple pieces of equipment at once, and to receive a repair estimate in the majority of cases, depending on your model and issue. The portal also allows you to upload images or videos that will assist us in repairing your product. You can also select how you wish to be notified of the progress of your repair. The portal's service history section allows you to view all services that have been performed on any of your camera or video products since January 7, 2020.
Please follow the link below to access our online repair portal to arrange for service:
https://mycanon.usa.canon.com/signin
Instructions for Accessing and Using the Online Repair Portal.
You will need to access or create your My Canon Account.
If you already have a My Canon Account and your product is already registered, simply click on the “Get Repair Services” link on the left menu and follow the onscreen instructions to arrange for service for your product.
If you have a My Canon Account and your product is not registered, you must register your product first. Click on the “Get Repair Services” link on the left menu, then click on the “Register Product” link on the right. After your product is registered, click on the “Get Repair Service” link on the left menu and follow the onscreen instructions to arrange for service for your product.
If you do not have a My Canon Account, you will need to create one. After you create your account, click on the “Add Product” link to register your first product. After your product is registered, click on the “Get Repair Service” link on the left menu and follow the onscreen instructions to arrange for service for your product.
Once you have completed the repair request, you will have an opportunity to print a copy of the request for your records. This request form will also contain shipping instructions and an address label that you will attach to the outside of your shipping box when mailing your equipment for repair.
