Not the author but I can answer your questions. Anyone can have a multilayer board fabbed by uploading the Gerbers to a fab house -- the board shows up on your doorstep anywhere from a day to a month later, depending how much you want to pay. Fine pitch SMD parts can be hand soldered with hot air and a binocular microscope; rework techs routinely do it every day.

I always tend to burn up PCBs when I try to de-solder broken parts with a hot air station. I usually use 300°C and a small nozzle... but always until the solder melts at the first pin, the PCB turns black-ish. What do I do wrong there?

Something I've found helpful is pre-heating the board (e.g., with an under-board IR heater) before breaking out the hot air. As another poster has mentioned, chip-quick is also great stuff.

If you're trying to de-solder a BGA component, I can't help, but any other surface mount stuff check out Chip Quik Alloy. It's a super-low melting point solder that you can use to take off pretty much any non-BGA component with a standard iron and a pair of tweezers. Cleans off with braid.

Why not use a plate/skillet for BGA desoldering?

Thanks for the hint!

Use higher airflow (including a larger nozzle) and lower temperature. The temperature calibration might be a bit off if the soldermask gets damaged by air at 300°C. Preheating, which has already been mentioned, also helps.

If you want a multi-layer board done up on the cheap (or fast, pick one haha) Oshpark is my go-to. They do 4-layer PCBs for $10/sq in.

Small Batch Assembly (haven't used them yet) should be able to put it together for you if you'd rather not DIY. If you'd like to, though, Osh Stencils, tweezers, some solder paste and a rework station (or a heat gun if you're feeling brave) and you can do a lot at home.

Also, designing a FPGA board is 'half' of the job, putting a verilog or VHDL code is a totally different thing.

The DDR3 routing, the BGA chip, everything on this board 'screams' very hard work, probably not by a single person ( i have to admin I checked the FPGA/board part only )

This could all be done by a single person. A very talented person, sure, but one person could do all of this.

I'm not certain about routing the DDR3 traces, but DIY soldering on a BGA chip isn't the absolute worst thing in the world, and VHDL/Verilog aren't that bad, especially when using the Xilinx tooling. A lot of that code is written for you (and you usually don't have to purchase IP cores... usually)

BGA soldering difficulty seems like somewhat of a persistent myth. Sure, it's difficult to get right if you want to solder a BGA as part of a production line and need to get 99.9% right or it becomes too costly.

But iPhone repair technicians and others are very blase about just using hot air guns and a ton of flux to solder all kinds of BGA chips, and they generally seem to work just fine.

Now DDR3 and USB3 routing is very annoying, but you generally just copy the reference design of the FPGA manufacturer and possibly adjust for your board layup.