Thanks Robert,

This display works like a charm in 4/8bits mode and this is why I now want to see how I can control it in SPI mode.

Humbly, I think don't even understand what I need to do to make it display something in SPI mode.

But you just gave me one more clue for a step forward:
The RS line is the command/data line. High being equal to data and low being equal to command
I read this before; the problem is, I don't clearly understand the st7036 controller's datasheet. This might be because I'm a hobbyist, not an well educated electronician

So, if I get it right, I should program something like this:
1.- set CS low = select the display as SPI target
2.- set RS low = select the "instruction" register
3.- send instructions = send "instructions" to the display (cursor position, clear, etc.)
4.- set RS high = select the "data" register
5.- send data = "HELLO WORLD"
6.- set CS high = unselect the target

Unfortunately, I'm in the office now and will have to be patient until tonight to try this

Meanwhile, if this process is somehow correct, how do I send a bunch of "instructions" or "datas" to the display? Is it a single "instr./data" @ the time? If "no", how do I send more than one info? Do I need to repeat all the steps?

What about the timings? In some examples I could find, one can see 25µs fudge factor? What is this for?

Last but not least: are my PIC settings correct in order to make the SSP work?