Translation:Is the cook cooking at the Italian restaurant?
Probably we have to think that the cook is cooking inside so choosing at the is a better choice
When it comes to places, how do we decide when to use -ben/-ban and when -nél/-nál?
'-ban, -ben' means inside something and '-nál, -nél' means close to something as a reference point. I suppose there are many exceptions but I think '-ban, -ben' is translated 'in' and '-nál, -nél' is translated 'by' in most cases (even in abstract phrases, for example 'in most cases'-'a legtöbb esetben')