How to set up Varnish to always serve content?

Question

Nginx

We set up caching on the frontend server using Varnish. All pages are cached for a short time (let's say 5 minutes). The problem is that Varnish starts showing Guru Meditation if the backend is more than ttl. The second problem is that with errors on the backend (uwsgi fell off and nginx issues 502), Varnish shows these errors.
I would like to make sure that the frontend server always gives users relevant content. Fresh, if possible, or old, if there is no other. How to do it?