This is not an easy question to answer, but I will give it a shot. First off, a flat plane crankshaft means all journals are on the same plane, so if you looked at it straight on it would have all journals in a line, straight up and down. A cross plane engine, when looking from the end straight on would look more like an X, evenly spaced.
There are many reasons to use one configuration over another. A flat plane design does not require counterbalance weights on the crankshaft. That allows for less inertia, higher possible rpm's, and faster acceleration. Although it is a little less refined as far as vibrations go. This is one reason this engine design is used in most V8 race car engine designs, but not used in most production cars.
Several factors influence firing order, but in a flat plane 90 degree V8 there are only a few choices. First of all, it depends on how the cylinders are numbered by the manufacturer. Some number their engines with number 1 on the right bank (1,3,5,7), number 2 front left (2,4,6,8) and so on, one accross from the other. Some have number 1 on the left front cylinder and number straight down that side to number 4 (1,2,3,4) and the front right cylinder is number 5 going back to number 8 (5,6,7,8) on the right bank. Ferrari numbers theirs starting on the right front with number 4, and continue on that bank 4,3,2,1. The other bank would be 8,7,6,5. In a flat plane V, regardless of the numbering system, the firing order always fires one bank, then the other bank. Notice the firing orders you listed. All have one side firing, then the other. All have numbers 1 and 4, 360 degrees apart.
Think of a flat plane V8 as two 4 cylinder engines put together, one on each bank. If you look at the firing order for the Ferrari, and the numbering system they use, every other number is on the same bank. This is the normal firing pattern for a typical 4 cylinder engine (1,3,4,2). The same is true for the other bank using the other bank numbers (5,7,8,6). This is the same pattern. Put the two together and you have their firing order (1,5,3,7,4,8,2,6). Because the V is at 90 degrees, this means each cylinder fires 90 degrees apart, and directly opposite on each bank. If you want to change the firing order, change the camshaft and it changes the order, but always 1 and 4, and 5 and 8 are opposite each other, as are 2 and 3, and 6 and 7. The numbers could swap order, but only in the pairs as shown (2,3 or 3,2 etc).
Another reason for this configuration, with one cylinder firing one each bank in progression, is that it helps with exhaust scavenging, keeping the exhaust manifold very simple to make, and does not require any crossover pipes.
I hope this helps with your question. There is more information available here: