How prevalent was the blackmarket?

Officially, everyone with the same job description had the same wages. This resulted in everyone becoming a slacker. So what eventually developed as a public secret, was that factories tolerated "theft" by the good employees.

So the person working in the canning factory brought home tins of food every month, which they would sell and/or trade. The boss could claim, and the books would show, that everyone has the same wages.

This is not limited to labour. Public administrators, for example, would be tolerated to put some people ahead of others for housing/holliday/etc, and they would ask for a fee.

It was a large, well known taboo that everyone, even party members participated in.

How many people actually believed in it? And how safe did people feel?

I can't speak for the early days. By the time I was born everyone I knew recognized it for what it was: the state as a weaponized tool to steal from and hurt others. An in-group of people decided how much equality and solidarity you deserve. You scratch their back, they grant you their leftovers.

Lots of the stasi files on people were shredded, and are intentionally slow being reconstructed, as they hope most people will be dead before they can read their own file. But estimates are that around 1-in-3 people were informants for the stasi. These are often neighbours, aunts, coworkers, ...

It was dog-eat-dog, and outside a small bubble you never fully trusted someone. Even then, no guarantees, as the schooling system (tried to) radicalize children into informing about their parents. The teacher would get benefits for each successfull "catch".