Authentication with JWT
Are there any security issues? Where should I store the secret's key,
  DB or InMemory? What's a good 'JWT' Lifetime? Should I send the 'JWT'
  in Header for every request? What should be done when a 'JWT' Expires?



The contents are merely base64 encoded and thus are simple to decode -- so don't encode your valued customers personal data.


cut and paste your token in here as evidence
https://developers.google.com/wallet/digital/docs/jwtdecoder


the secret key is not a session one so in memory makes no sense. buy an oracle license and then stick it in there. or theres nothing wrong with something nice and simple like this.

    const string algorithm = "HS256";

if you're logging a user onto a site. 1 hour? its possible to copy/paste the token and gain access to data. so it depends on the nature of the data. 
yes. its an awesome method to send to a REST server instead of some internal userid that never expires
kick them out of your site. make them relog in and get a new token (with another hour long token)