There has been some work gone into GC games, not so much in translation though.http://hitmen.c02.at/files/yagcd/yagcd/frames.html
is the main hardware documentation for this, however it is a bit old so you might also want to poke around the dev notes/wiki/source code to Dolphin, https://github.com/dolphin-emu/dolphin
for the source and https://dolphin-emu.org/
for the rest.
The formats are broadly similar to a lot of what was seen on the Wii (the Wii was basically an overclocked gamecube so that is a common theme) and to a slightly lesser extent the DS (the DS is a bit more limited so some of the common things seen on the GC would serve no purpose on the DS, anybody that looks at the GC ARC format and the DS NARC/CARC format can attest to that). YAGCD above covers a few of the common formats as well (chapters 14 and 15) but not in any great depth.
Being optical media based* you do have a filesystem to play with, the tools are not quite as nice as some of the stuff seen on the Wii as far as remapping and general niceties but pulling files out, injecting them back in and otherwise building isos is quite possible. GCtool is probably the more common one here,
The GC did seem to pioneer or at least make common a type of compression called yaz0 ( http://www.amnoid.de/gc/yaz0.txt
), it became very popular on the Wii so you are better off looking there for tools, not sure what the current one is there as I tended to just use the example builds of various libraries floating around. Tools wise there is enough that someone that knows hacking well enough could get by (GCtool does iso stuff, yaz0 is sorted, IDA has reasonably modern plugins
for the DOL format that binaries come in, you can do worse than dolphin for an emulator with debugging though it is certainly no FCEUX....), you have nothing really as far as some of the far nicer/more extensible stuff those playing in NES and SNES world have though.
I would really not suggest the GC if you "have no experience at all whit the translation of videogames". It sounds like you have a fairly basic game on your hands but if it throws a curveball at you, hands up everybody that has had the majority of their projects be basic formats without any quirks at all, then you are going to be learning a lot to get past it and there are not going to be so many people able to help you; if it did not say mario kart or smash brothers on the title screen then it probably was not hacked very much, GC homebrew was never really a thing and we are still seeing massive improvements to the quality of GC emulation.
*do be aware that a lot of work went on in the Wii side of things and GCOS before it, to this end if you are downloading games then they might not come in standard ISO formats -- with the failure of the GC and success of the Wii many people went back and looked at what the GC had to offer, for reasons unknown they then rebundled said isos in other formats. There should be tools to extract/convert things out of these formats (Gamecube ISO tool and maybe GCMutility being two popular ones).