Focus/fast charge skill affects switch axe sword gauge too. As it's widely known focus lets hammer/gs/bow do charge attack faster, but it makes the gauge for ds/ls/sa fills up faster too. In sa's case, the gauge will autofill faster when you're in axe mode or sheathed.

As for reloading speed skill, pretty sure that's a gunner specific skill that only affects bowguns.

Altho manual reloading the gauge when extremely low isn't really that slow but in all honesty, you shouldn't really be doing manual reload of sword gauge in the heat of battle most of the time. Just like how you wouldn't be eating a potion or sharpening your weapon unless there was a big enough opening.

By balancing both axe and sword form usage, the natural regen rate of sword gauge is pretty sufficient. Just remember to keep track of the gauge and dont keep slashing in sword mode once its almost ran out because you'll auto do the switching animation back to axe mode if it runs out during the middle of your slash combos. That delay is enough get you run over by the monster whereas you could have roll/sidehopped away otherwise.

In case anyone didn't know, you can quickly switch forms in the middle of a combo. When in axe mode, pressing R after doing forward stab with analog+triangle will switch to sword mode. In sword mode, attack with circle to do the sideway slash and press R will quick change into axe mode.