Never. I entered Dental School in 1964. In all that time there have been exactly zero cases of toothpaste overdose reported in the dental literature. It's a non-issue, so please don't worry about it.
Death? Are you allergic to toothpastes? If there is an ingredient you're highly allergic to, you can respond in an anaphylactic way, but that's highly unlikely.
Not an issue. As mentioned above you would get nausea and upset stomache but wouldn't die. The main concern is too much flouride, but you'd still need to ingest a full tube for any significant negative outcome.
Unlikely. All toothpaste is, is soap and sand. You would get very ill and nauseous before you ingest enough to kill you.