Short shifting can help if you need to adjust the cars balance, if power is being delivered too fast and the car is unstable then it can sometimes be a better option to shift up rather than come off the throttle, how beneficial it to to maintaining grip while accelerating depends on the rate the power is delivered in the gear you've shifted into. I wouldn't say it's not useful, it's just more complicated to say if it is and how since it depends on so many variables.
Down shifting might help in slower corners but your speed needs to match the gear you're down shifting to, you don't want to down shift and suddenly have the needle bouncing off the limiter, It may help if you down shift and the revs are high but if you do it too soon and the revs are hitting the limiter then the rate of engine braking can again destabilise your car.
I think the thing you need to work on is keeping the car balanced by staying on the throttle as much as you can, even when your braking you don't always have to come completely off the throttle, don't get too caught up in the gears yet, you can get the wrong gear and keep the car balanced by good throttle and brake control much easier than getting the right gear and making a mess of your throttle and brake control. Perhaps try to ease off the throttle as you brake but don't come off throttle completely. Try doing this to varying degrees and see how it changes the cars balance.