Electronic – Write into external registers from FPGA

Your FPGA design is using the fall signal to clock out data on MISO. But its probably using rise to clock data in from MOSI. The microcontroller will do the same thing. It knows the falling edge of SCLK is telling the slave to change the MISO line, so it won't clock that data in until the rising edge of SCLK. You have to be sure that your FPGA clock is fast enough that even with two clocks delay on detecting the falling edge, it will be presenting valid data to the microcontroller by the time of the rising edge.

This arrangement not only gives your slave device some leeway in how quickly it responds to SCLK, it also allows for some uncertainty about whether the SCLK or the MISO traces or cables are the same length. By sampling MISO in the middle of its valid period, you allow the SCLK transmission delay to be either longer or shorter than the MISO transmission delay. Another way to say this is that the SPI receiver is designed with balanced set-up and hold times.

This is different from the way you normally arrange data transfer between gates in your FPGA. There, your flip-flops generally have zero hold time. That is, they clock old data in on the same edge when the upstream flip-flop is changing its output state. They can do this by delaying their data inputs just a little bit more than their clock inputs, and its an arrangement that generally gives the best possible maximum clock rates while still being relatively easy to guarantee the timing with automated tools.

The balanced set-up and hold arrangement on SPI can't achieve the same high clock rates as the interfaces within the FPGA, but it also doesn't require anywhere near as careful management of the propagation delays between the sender and receiver.

You can't properly describe an LVDS receiver or transmitter in VHDL. LVDS interfaces have electrical requirements that typically cannot be met by just using plain digital input and output pins. Your FPGA needs to have dedicated input and output macrocells for those functions and you would just instantiate them. Exactly how that is done depends on the exact FPGA and toolset you are using. Within the FPGA, there is just one signal that would come from the LVDS receiver and one signal that would go to the LVDS transmitter.