Honestly, if you are satisfied with your current keyboard, why build a custom one? If you choose only what you are used to, you will end up building the exact same keyboard you have now.
Answering your questions:
How hard is it to build one and get them working?
It is definitely not an easy road, but I am sure 99% people out there could manage that. There are hundreds of guides and videos about building a keyboard online. You might even be interested in some of the build logs people post. After all, if you are not going for a high-end keyboard burning a PCB is nothing terrible.
Are there any 104 key layouts?
There are really few full-size boards available, with 1800 layout (KBDfan's KBD19X, Massdrop's Shift) being the closest ones. The reason is that practically nobody "needs" keyboard that big. Full-size keyboards don't really give you many benefits, but are less ergonomic (asymmetrical in design, which requires tilted body posture), harder to work with (less space for a mouse, need to move hands to reach certain keys), harder to transport, harder and more expensive to build, and, imo, just look worse. I am sure most people can get away with at most TKL keyboard, with 60/65 keyboards being the sweet-spot.
If you *really* need numpad for entering numbers and don't want to use numpad on keyboard layers you are better getting separate numpad, not a full-size keyboard.
How fast and how bad is the shine on a GMK keycap set.
That's really personal. Depends how heavy you use your keyboard and how much you dread shiny keycaps. Some people actually enjoy shiny look. IMO it's really not bad at all, and just proves your love to certain keyset. After all, you don't need to keep that one keyset and replace it as soon as you start hate it, or you could even try to sandblast your keys.
https://deskthority.net/viewtopic.php?f=7&t=12946&start=I can't tell how much losing backlit keyboard will be for me.
You should be touchtyping anyway. Not seeing actual letter on a keyboard actually pushes you into learning those weird key location.
Any good switches that are similar to Nature Whites?
Switches are as personal as it gets. Most people would recommend you to get a switch-tester, but if you like a particular switch on a tester does not mean you will like it on a keyboard. If you enjoy linears I'd suggest Gateron Yellows or Gateron Inks. Both are pretty good starter linear options, but you definitely need to investigate yourself what works for you better.
Some people prefer to buy hotswap keyboard to try-out and swap different switches. That might be an option for you.