How to set up W3 Total Cache on a dynamic WP site?

Question

caching

There is a site on which it is assumed that a fairly frequent change in content / adding new content.
I used to use WP Super Cache, but for some reason it doesn’t want to work on nginx - it can’t open the cached page, just a white screen.
I installed W3, everything seems to work, but not quite as we would like, for example, the name of the registered user is displayed on the main page, and the page is saved in the same way, with the same user. Those. I logged in as user 1, logged out, logged in as 2, and it shows me that I'm under 1, although in fact under 2. This was not the case in Super Cache. Also in SC, after adding a new post, the cache was automatically updated, W3 can't do this?
Maybe there is some instruction for my case?