First of all, the alerts that we display are in no way blocking the use of your signatures / campaigns. They are only recommendations on our part.
First case :
This means that the signature may be cut off and/or unreadable when the email is read from a cell phone screen (if it is wider than the 300px to try to fit the screen size).
Second case :
This alert only applies to signatures deployed with the push API for Gmail.
This is because it limits the number of characters contained in the code of a signature to 10k. These are not only the contact information you can see but also the code of images, links, generated HTML code, etc.