I would like to know more about how the Turbo Core of the N64 works:
Only increases the framerate
Only increases the game speed (how fast you move in terms of distance per time)
Both
So for example if I do a speedrun with the core in turbo mode, will take less time than the original console?
I'm sorry to say it is a resounding; it depends.
It will widely increase the framerate across the board. In some games where game logic/physics is tied to framerate (it was pretty common in the 90s) you will find that some things, including player movement, may behave relative to the how much faster the game engine is running.
It's probably safe to say speedruns would be illegitimate on both the regular and turbo cores due to speed/timing indiscrepancies.
Robert said this on the latest release
same as above, overclocked components: RSP/RDP 62.5->80mhz, CPU 93.75->120Mhz, DDR3 125 -> 160Mhz
VI and CPU Timer speed is adjusted to let most games run at the same speed as the normal core but with higher fps.
Don't report bugs with this version, only use for fun
Some games (for ex. Ocarina, Majora's Mask) require patching with the Patcher64+ Tool with 30FPS option enabled in order to get the higher frame rate. But there have been reports with Ocarina at least (don't know about Majora) on the Discord, of the 30FPS option causing certain glitches, possibly game-breaking, as certain actions and certain animations will not work properly at the higher frame rate.