Does each protein adopt a single specific structural motif (zinc finger for example) or are there any proteins with multiple motifs along the chain?
Most large proteins contain multiple motifs; if you search online for pictures of protein structures, this should be immediately evident. Here's an example from something I was working on the other day: the WD40 repeat motif. It appears in many proteins, but those proteins are certainly much more than a bunch of WD40 units. If you investigate some of the proteins listed at the bottom of that Wikipedia page, you should be able to confirm that they are complex and made of many different sorts of domains, shapes, and parts.
You also mention zinc fingers; those are a DNA-binding motif that show up in many, many different DNA-binding proteins. Those different DNA-binding proteins have many different functions, and their specificity is handled by a vast array of different sorts of motifs and domains that sit on top of/outside of the zinc finger itself. The Wikipedia article on zinc fingers shows many different structures in which zinc fingers can be embedded, and even those structures are only small parts of the actual functional proteins that perform work in a cell.