First off, Tor is not the Tor Browser. Tor is the onion network through which the Tor Browser (and any other client, for that matter) connect through.
> When should normal users not use Tor?
Since Tor has drawbacks such as speed, it may prove impossible or at least difficult to use Tor all the time. If you really want the extra anonymity, go for it.
Personally, I don't care if Google keeps a tally of all my searches and piles cookies on me, I enjoy personalized search results. Anonymity is useful sometimes though.
You could definitely use it 100% of the time though.
> Should it always be used with a VPN?
Tor provides an onion network, I don't see a need to ever use a VPN.
> Should normal users use a different browser when accessing personal accounts (banks, email, shopping)?
The Tor Browser doesn't keep cookies and other identifying information, so it's as if you're using a fresh browser each time you access these services. Security-wise, SSL will encrypt banks and email (most likely). So accessing those services in a normal browser doesn't inherently put your privacy at risk.
> What are the problems with using Tor as my only browser?
Speed issues, as the network is pretty slow at times.
Otherwise I can't think of anything really.
NOTE: I'm not an expert on Tor, I'm just speaking from personal experience.
