Is it possible to install and run Windows 10 IoT on an "regular" workstation/device/PC? With this I'm talking about an old laptop which I want to use as an IoT Device just running a website (or maybe an app) [display unit of my smart home system] but don't need all the overhead from Windows itself.
The list of supported hardware for Windows 10 IoT shows which devices are currently supported. The majority of these are single-board computers and the like, rather than regular PCs. Notably, though, some lower-end CPUs by Intel are supported — mostly products of the Atom, Celeron and Pentium range. It may be worth checking what hardware your device contains, as if it is listed, you might be able to use Windows 10 IoT.
If, however, it turns out that you can't use Windows 10 IoT on your device, you might find it more convenient just to install a lightweight Linux distribution. Depending on how confident you are, you could install something well-known such as Ubuntu or something more basic, such as Arch Linux, which will involve you installing and configuring many aspects of your OS, including desktop environment etc.
If you use something like Ubuntu, there'll be a reasonable overhead as you'll still have a GUI, but perhaps less than Windows. If you use Arch and only install exactly what you need (i.e. no desktop environment, few unnecessary services), you'll get a lot less bloat.
Yes, Windows 10 IoT runs on any x86 or x64 processor running faster than 400 Mhz and 256 MB of RAM. The SoC compatibility list is for the unusual and non-x86 processors that it supports.
Windows IoT Core only supports running a single UWP app that launches at startup, which could work for your webserver use. IoT Enterprise supports a more typical Windows desktop experience.
Windows 10 Home is less resource intensive than Win 7 and usually performs about as well as Windows XP, which as released in 2001, so if your machine is < 15 years old then plain old Windows 10 should function on it.