Solve problems using bitcoin smart contracts
What will be the best way or resources to refer if someone has an idea and want to implement it using bitcoin smart contracts?

If smart contracts involve the use of external data (oracles) then Discreet Log Contracts are the best possible way.

How would I approach solving this problem using bitcoin?

I have mentioned few points in this doc, it won't be easy creating an oracle that decides if someone is dead or alive, create incentives around it, use of funds, exception handling etc. however nothing wrong in trying: https://docs.google.com/document/d/1baOWfya2mqd3ZAoDS4a2VQlb3-q4JCILXRN-oe4_zOk/edit

What are best resources to learn more about discreet log contracts, it's examples?

DLC channel in Lightning Dev Kit slack :https://lightningdevkit.slack.com/
Examples:
P2P Derivatives: https://github.com/p2pderivatives/p2pderivatives-client
https://medium.com/crypto-garage/step-by-step-guide-p2p-derivatives-application-c0454606428e
Benthecarman is working on a project which can be used to experiment with DLC (scala):
https://github.com/benthecarman/krystal-bull

Nicolas Dorier is also working on NDLC and I tried a creating a GUI for NDLC-CLI using C#: