The Richelieus were not the only battleships to have all their turrets forward - and quadruple turrets were not the only ones used for such designs. The British Nelsons, and their unbuilt G3 and N3 ancestors, used triple turrets in an all forward configuration. As I'm more familiar with the Nelsons and the design decisions that went into them, this answer will be considering them more than the Richelieus.

The main draw for the all-forward configuration was the saving in length, both overall and in the citadel. Length was a serious limitation on a battleship - if it was longer than the available slipways or dry docks, then it couldn't be built or maintained without a costly expansion. The first RN designs in the process that would end with the Nelson class, the L2 and L3 (and the K2 and K3 battlecruisers), were conventional designs, but were pushing the limits of what could fit into the dry docks at Rosyth and Portsmouth. Switching to an all-forward design meant that the boilers could be relocated aft next to the engine rooms, reducing the complexity of the machinery and pipework. This relocation also allowed for a reduction in overall length for the same speed. Switching to an all-forward design in the M2 and M3 designs saved ~1500 tons over the L2 and L3. If the all-forward design was built to the same dimensions, this extra weight could be used on armour, armament or engines. As you note, the relocation of the boilers and concentration of the turrets forward reduced the length of the citadel. This was both an advantage and a disadvantage. The citadel armour could be thickened, or the weight savings could be put into something else. However, the reduced citadel length meant that a lower proportion of the waterline was protected. This was a threat to stability if damaged, as the protected reserve buoyancy was concentrated in a much smaller area - if the unarmoured areas were flooded on one side of the hull, they could overwhelm the reserve buoyancy in the citadel. None of the all-forward designs produced by the RN met USN standards for damaged stability.

As to the armament, the British designs used three triple turrets. The aftmost was not superimposed, and therefore was obscured when firing forwards. This was, of course, not a problem faced by the Richelieus. However, blast effects were a major problem on the Nelsons in action, and would likely be on the Richelieus too (though the serious weight saving on the Nelsons, in order to meet Washington Naval Treaty standards, exacerbated this problem). Firing aft of the beam meant that a significant portion of the blast impinged upon the superstructure and hull, damaging fragile pipework and instruments. When Rodney participated in the sinking of Bismarck, blast from her own guns did much more damage to her than Bismarck's. Many lightbulbs, water mains and toilet fixtures were demolished, furniture and lockers were dislodged and thrown about the ship, bolts and rivets were loosened causing leaks and framing beams cracked, all by the blast. In practice, this tended to limit the arc of fire capable of the guns. Quadruple turrets were rather advantageous. Firstly, they reduced the area of the ship taken up by the turrets, making it less likely the turrets would be hit. Secondly, they reduced the weight needed for the turrets. This could either be used to compensate somewhat for the lack of stability inherent to the all-forward design by reducing topweight, or to increase the armour on the turrets. However, the large holes in the hull did cause certain problems. As the ship flexed, the diameter of the holes changed (and with a larger hole, this change happened much more). This was the main problem with the turret mechanisms on the King George Vs - the tolerances on the quadruple turrets were too high to cope with the flexing.

Was the accuracy problems to firing directly in front ever resolved? If I understand correctly, the formal term is called Canted Trunnion Error, and there was later better fire control in the form of Cross Leveling Gear for firing directly in front. Were there any other accuracy problems inherent with the 2 turret design that could not have been resolved with better fire control?

Cross Levelling Gear was available on fire controls available at the time the Richelieus were being constructed - early examples were being fitted to RN ships in the late 1910s and early 1920s. However, until the 1930s, this did not fully include feedback from the turrets to the director, limiting its effectiveness. Modern versions were fitted to RN ships from 1939. Even without it, methods did exist to reduce the effect of roll on fire over the bow. However, the Nelsons and the Richelieus were intended to fight mostly broadside-on, not firing over the bow.

That said, the hoists themselves on the French battleships weren't too good, and I suspect that with far better hoists, the rate of fire would have matched other battleships like the Bismarck.

This isn't quite right. The main reason why Bismarck had such a high rate of fire was that German guns used brass-cased one-piece charges. These made storage and handling trickier, but meant that the loading cycle was quicker, as the only a single charge had to be loaded. It's also worth noting that the numbers typically cited for Bismarck's guns are under ideal conditions - at Denmark Strait, Bismarck had a rate of fire of under one round per minute per gun. This was partly due to faults in her hoist design, which could cause breakdowns. During a May 1941 test by the German AVSK (Artillery Testing Command for Ships), her hoists suffered two major breakdowns, both requiring a significant time to fix.

I wonder if it would be possible to complete automate the reloading process in a way kind of like the Des Moines class, built just after WW2.

No, completely automating the process requires a turret built from the ground up for it.