The battery of the GoPro 4 is not compatible with the GoPro's 5/6/7/8.
The charger is also not compatible.
The batteries from the GoPro 5 onwards are somewhat thicker and have 4 pins.
Not necessarily. You can also simply charge the battery in the GoPro as usual.
Otherwise, you can also use the following external battery charger: GoPro Charger for 2 Batteries for Hero 5 / Hero 6 Black (Charger, Battery)
Alternative with 2 spare batteries included: Wasabi Power Dual Charger with spare batteries for GoPro Hero 5/6 (battery, charger)
The Hero 8 has a revised image stabiliser, and generally much higher maximum power loss, which requires a more powerful battery (maximum current, not capacity). The Hero does not need the battery for the Hero 8 in this respect. I myself need the battery for the Hero 7 even with my 8 Black, then I simply can't use certain functions.
I tested the battery today on the Hero 7 black. I was able to record 4 recordings of approx. 17 minutes in 1080p@60hz.
However, it depends on whether you are recording in FHD or 4K.
Yes they also work with the 8. However, there are a few restrictions on the functions. The camera indicates this when the "old" batteries are inserted.