I omit water requirement as not important.
Should you crack oil?
You can transform 2 heavy, 2 petroleum or 1 light to 1 solid fuel.
You can crack oil products: 4 heavy → 3 light → 2 petroleum.
Heavy oil gives you 0.5 solid fuel per heavy unit. Heavy cracked to light gives you 0.75×1 = 0.75 solid fuel per heavy unit.
Light oil gives you 1 solid fuel per light unit.
light cracked to petroleum gives you 0.66×0.5 = 0.33 solid fuel per light unit.
Result: You should crack heavy into light, but avoid cracking light into petroleum.
Basic or advanced oil processing?
Best values you can get per oil product unit: heavy → 0.75 solid fuel, light → 1 solid fuel, petroleum → 0.5 solid fuel
Basic oil processing gives 3 heavy, 3 light and 4 petroleum per 10 crude.
Advanced oil processing gives 1 heavy, 4.5 light and 5.5 petroleum per 10 crude.
Total solid fuel per 10 crude:
- Basic oil Processing: 3×0.75 + 3×1 + 4×0.5 = 7.25 solid fuel
- Advanced oil Processing: 1×0.75 + 4.5×1 + 5.5×0.5 = 8 solid fuel
Result: It is better to use Advanced Oil Processing to maximize solid fuel yields.
Not in vanilla, afaik. You've got to work around the set inputs. Hopefully this changes at some point, but for now, there's nothing you can do besides modding the game.
And speaking of modding, I believe this mod will do what you want for inputs at least http://www.factoriomods.com/mods/gdiw-gha-darnitwater
Best Answer
Does the choice of oil have any impact on turret performance?
Yes. Heavy Oil gives 5% damage bonus, and Light Oil gives 10% bonus.
Which one is the more economical choice regarding crude oil consumption?
As Oil Processing produces large amounts of Petroleum (at least 40% of output), which is not useable in flamethrower turrets, and rate of fuel consumption does not change with fuel type, crude oil will be most economical choice.
What fuel should I use?
If you are interested in most economic choice, Crude Oil is the fuel of choice. If you want most DPS from your turret setup, use Light Oil. In most practical setups, there would be noneven ratio of production/consumption of different oil products, so you are probably want to use what you have in excess.