Hello Asimo_robot,
Welcome to Apple Support Communities!
If we understand your post correctly, you're unable to add your email accounts to the Apple Mail app. We'd like to help!
For help with adding your iCloud account to the Apple Mail app check out the steps in the article below.
Set up iCloud for Mail on all your devices
Also, check the iCloud.com website to see if you're able to send and receive mail. Follow the steps provided in the article below.
Use Mail on iCloud.com
The article that you came from, If you can't receive email on your iPhone, iPad, or iPod touch, does give steps for not being able to add an email account. These steps would be helpful for the Gmail account.
- Contact your email provider or check their status webpage to see if there's a service outage.
- Ask your email provider or system administrator if you turned on any security features or restrictions, like two-step verification, for your email account. You might need a special password or may need to request authorization from your email provider to send and receive email on your device.
- Check your email account settings with your email provider or system administrator to make sure that they're correct."
Let us know if you have any questions.
Thank you for using Apple Support Communities.
Take care!