Up to how many nodes Drupal can handle without affecting performance? Is there a kind of known number of nodes Drupal can handle without visible performance down? 

I suppose the more nodes we have on a site the slower it will load pages. However does it matter if the number of the nodes is like a couple of thousands?
It very much depends on your hosting and server configuration. 

For example one of the projects I worked on handled without performance issues about 10 millions of nodes. But it lived on a cluster of 4 dual-core servers with lots of memory on each, and the cluster was behind load balancer and reverse proxy caching (Varnish). 

On another project I had performance issues after something like 1000 of nodes, that was a shared hosting.