I have an Altera Cyclone IV FPGA (for ie) and my question is: is it possible a raw programming of the FPGA? Is it possible to set "manually" the gates for making experiments?
Surely if you were able to fully comprehend and become knowledgeable of all of the following factors regarding a particular FPGA it would be possible to hand craft programming files for the device.
I have probably left out a basket full of additional details that would be very important to be familiar with that would play into making successful hand coded designs. Timing and delay compensation come to mind here.
It should become obvious very quickly that there is a reason that FPGA vendors provide development tools to cover almost all of these details. Using a recognized standard description language to describe the function intended for an FPGA design makes your intellectual property portable to almost any FPGA. Trying to understand what you have asked about regarding hand crafting a programming file is easily 20 to 30 times the work and would only be usable on one or two devices in some specific FPGA family. I suggest that your energy would be much more well spent becoming an expert at usage of the standardized description language.
If part of your curiosity is a drive toward becoming a designer/creator of FPGA components themselves then I suggest that you start by focusing on one particular aspect of the technology and learn that. If you had a job at one of the FPGA houses you would be part of a large team that includes dozens of skillsets that all come together to produce the FPGA products and tools that you will find in the market today.