How do different methods of connecting USB-C display work? There are multiple ways how we can connect an external display via USB-C to an Apple device (say MacBook Pro). For example:


directly (e.g. LG UltraFine)
using Apple's USB-C to HDMI/VGA/DVI dongle
using a USB-C dock that supports DisplayLink


The last mentioned method - DisplayLink dock - is a 3rd party solution that does not seem to be supported by Apple and requires special drivers to be installed. Do other methods also require special drivers?

Is using original Apple dongle or connecting a display directly better since it connects directly to GPU while DisplayLink needs to encode/compress the image? (I've noticed it uses substantial amount of CPU).
Is using original Apple dongle or connecting a display directly better
  since it connects directly to GPU while DisplayLink needs to
  encode/compress the image? (I've noticed it uses substantial amount of
  CPU).


The short answer to this is yes.  DisplayLink is the "universal" USB display adapter driver. Being that the adapters are USB devices, and not actual GPU's, it stands to reason it will use more CPU than the other methods.

USB-C

The industry and Apple have created a ton of confusion around USB-C, Thunderbolt, and DisplayPort.  So, let's clear some of it up....


USB-C is just the connector type.  Technically, it's called a type C connector.
Thunderbolt 3 utilizes a type C connector and includes the following signaling:


DisplayPort video 
USB 3.1
Power Delivery
PCIe

A USB-C port is a type C port and includes only the following signaling:


USB 3.1
Power Delivery
Optional DisplayPort (like on the MacBook without Thunderbolt Ports)



So, it is entirely possible to have what looks like a USB port be a Thunderbolt port that supplies video and on the other end of the spectrum, have that same looking port provide nothing but USB connectivity.  This, along with calling everything now "USB-C" leads to tons of confusion.

USB vs. DisplayPort

The first two methods, you described, connecting to the LG UltraFine or using Apples HDMI/VGA/DVI adapter both utilize the DisplayPort signaling embedded within the port to connect your GPU (integrated or dedicated) to your monitor.  It's a pure video signal.

A USB dock (regardless if it uses a type A, B, or C connector) is a USB device, not a DisplayPort device (caveat:  unless noted that it actually passes the DP signal).  Consequently, a USB video device is "created" and driven by the CPU, not the GPU.