I just started using PowerApps myself but I think I have some insight to your questions.
- The app will be a "desktop first" (or browser first) app, using the app on mobile devices is not necessary at all. Is this possible? (hard requirement)
Powerapps can be run straight from the browser or used within the actual powerapps (windows 10 only?) so yes, you can definitely make it more for the desktop first. On my desktop the browser version is identical to the iPad app version.
- Can i create a (relational) database in Powerapps, consisting of several related tables and several different queries? (hard requirement)
From what I've seen the short answer is kind of. PowerApps allows you to build collections/tables similar to Access, but honestly I've been using SQL as the backend and it's considerably easier to work with to build proper relational databases. PowerApps isn't a database program at it's core, but it works with many data sources and I think you'll find it's very limited.
My suggestion is get some test data setup and play around in it to get some idea of PowerApps limitations (there are many!)
- Can i link a table (or a query) to an Excel workbook which resides on our local network so new records are automatically added tot the excel workbook? (new feature, would be very nice)
Yes, there are some options to link directly to Sharepoint stored excel sheets but not network shares. It would be worth trying it out yourself to again see what limitations it has but I've had success setting up an excel sheet as a data source but it has to reside in an acceptable location for PowerApps to link to (i.e. Sharepoint).
I would suggest looking at SQL since you can setup a "linked server" directly to a shared excel workbook and effortlessly pull data in from there.
- Can i add Word (2016 desktop) templates to Power apps so my users can search a client in our PowerApp and create a letter where the name and address of the client are already filled in? (new feature, would be very nice)
I think you will find this won't work but you may find a solution to pulling data in but from what I've seen you cannot even print from PowerApps at this time.
Hope that helps a bit!