First off, I'll look at the explanations you have found.
- leftover energy from the Earth's formation
This is typically split into two parts, the energy from the collisions that formed the Earth, and the energy from the differentiation of the proto-earth into a core, mantle and crust.
- radioactivity of the elements inside the core
This is highly debated. Geophysicists and geochemists agree to disagree. Geophysicists want a rather high heat flux across the core-mantle boundary because their geodynamo models (which aren't quite perfect) demand it. Geochemists say otherwise. The problem is that the three elements (uranium, thorium, and potassium) that provide four long-lived isotopes are incompatible elements. Moreover, uranium and thorium can be ruled out as sources of core heating due to geoneutrino observations. The neutrinos emitted by potassium decay are not detectible by current technology. Perhaps potassium behaves very differently under very high pressure and temperature.
- friction between the core and the more outer layers which spin more fast
I'm not sure where you found this. As a general rule, it's the other way around: the core spins faster than the mantle. The mantle and crust are subject to tidal torques from the Moon that is gradually slowing the planet's rotation rate. The vast majority of this slow down results from interactions between ocean tides and the Earth's crust. This in turn makes the mantle rotate ever more slowly, and that in turn makes the core rotate ever more slowly. That said, this is a small contribution.
You missed a key component, which is
- the formation and growth of the Earth's inner core
A liquid freezing into a solid is an exothermic reaction (a reaction that releases heat). The ongoing formation of the Earth's solid inner core adds heat to the core.
However, I haven't found any indications that would point to the high pressure being a factor. So does the large pressure inside the Earth's core contribute to its high temperature?