I'm going to start with the bonus question - why were motor driven cannons not explored during the war?
The reason engine* driven guns were explored in WWI was 2 fold:
1. Machine guns were relatively new and not overly reliable - hence the gun within reach of the pilot to clear jams. By using the power of the engine, the mechanism of the gun could be guaranteed to cycle.
2. Synchronization - As the propellers were fixed pitch, the engine speed varied greatly from climb to cruise to dive. Again, by driving the mechanism by the engine, you guarantee the gun only fires when the propeller is out of the way.
Solution 1: Machine guns very quickly because more reliable (and the power of the engine often made the jam worse)
Solution 2a: Largely the electrical engineers, either by solenoid or electric primer, resolved the synchronization problem.
2b: Propellers changed to constant speed, greatly simpilying the problem - with the engine only turning a set speed designers have more leeway in firing.
*Note 1: I changed the answer slightly from motor to engine.
As for sleeve valves, everyone so far has missed that they smooth out engine vibrations (Going into a little extra depth for your engineers)
On a single cylinder engine**, you want counter weight to balance the weight of the crank throw (where the rod is attached).
But you also need balance weight of the big end of the rod, so you put the rod on a scale and weigh the big end and add that to the crank throw
Then you do a bunch of math to determine how much of the weight of the small end of the rod/piston you want to balance.
But you can't win - you will either have vertical (same direction piston is moving in) or horizontal imbalance. In most cases, you pick the lowest weight because extra material causes all sorts of knock on issues.
With sleeve valves, you have the sleeve going up and down in the cylinder bore. By properly adjusting the ports in the sleeve, you can "time" the sleeve, so its motion is opposite the piston.
The result is a very smooth running engine = quiet.
**Note 2: Inline 6 cylinder engine (and V-12, arrow 18, X-24 are all multiples of Inline 6) is statically balanced without any counter weights!
Now, while it is statically balanced, there are torsional forces as the cylinders go through the firing cycles - so you will need to analyze where better to make a crank with larger bearings (to resist the torsion) or some counter weighs which allow smaller bearings.
This is where engineer earn their pay as there is no "right" answer <but there are lots of "wrong" ones>.
As for connecting rods.
When you use 2 large bolts versus 4 smaller bolts:
a. You concentrate the load
b. The larger bolt is more apt to have material imperfections, so you need to 'de-rate' the strength.
Which is why you see the articulated rods which
S
Shortround6 has pictured.
But they have the issues with balance - the articulated rod doesn't follow the same centerline as the crankshaft. Again, the issue is minimized in a V-12, but its still there demanding a heavier crankshaft and better bearings.
As for the blade and fork. As has been the theme, if you center the load on the bearing journal, you can minimize the stress on the crankshaft = lighter crank = lighter engine = lighter airplane.
There is also a secondary advantage - the blade rod holds the fork rod big end round. At mid stroke, there is significant sideway force on the rod, which results in the bearing becoming less than perfect circle - which can result in pinching out all lubrication... Which is why the forked rod in the RR V-12s is of 3 piece construction***. The significantly larger diameter of the blade rod doesn't have the same issue - but if RR made the crank with rod journals the size of the forked rod, it would have been very heavy.
Note 3: Junkers did a more elegant solution of a simple cut in the rod to minimize the lateral force - which could be applied to both the blade and fork rods, allowing them to get away with just 2 piece rods (main rod and cap) The same Junkers solution is used to today's F1 engines (per Callum).