They can't make you prove a negative, is the thing. Even if they wanted to deny your payout, you would just sue them in small claims court (as the beneficiary) and you would be well under any jurisdictional maximums for small claims court that would cause it to go to any higher level court. Once again, it becomes cheaper for them just to pay you. If they don't want to pay you, then they would have to send someone to appear and defend in small claims court...but if they don't...the person suing them wins a default judgment due to the failure of the other party to show up.
I don't know that they can force you to provide medical records at all without a court order, but even if they could, they couldn't force you to provide records that predate the policy. That's why more legitimate insurance companies for higher dollar amounts want to see that information beforehand, usually. The difference here is Globe Life is designed to be a rip off, but that also presents the opportunity to use their own angle against them. That's what AP's do at casinos.
No, they have to pay based on the questions answered or it goes to small claims. If they want to defend not paying you in a small claims case, it's incumbent upon them to prove that you lied on the questions. The Plaintiff can certainly prove that Globe Life agreed to insure them for the monthly premium. They could subpoena any records that predate the policy, but again, you get into things that cost them more than $1,000 or even a couple thousand bucks to do.
Depends on how soon you die. If you die within the first year, your value was terrific.