You probably don't notice your back arching as much when standing, as it's easier to keep it in neutral when seated, it's why i recommended it

Youtube a prone TVA exercise to help you combat this. 1 x 10-20 daily is acceptable. Recline the seat a click or two to make it easier, don't go too far back though. If it's still not working roll up a small towl, wedge it into the gap, and work on keeping tight to that.
The click you can feel is called crepitus and is likely a result of anterior impingement (the shoulders rolling foward, scapula winging, and all the bits at the front getting compressed) being seated helps promote a more neutral shoulder as long as posture's good so its probably why you don't feel it. Shoulder mobility will definately, definately help. Start by rolling, then stretching the chest and lats.
Try doing the lateral raise standing, but starting with the weights in front of your body, almost resting on your thighs. When you raise the weight, come up and bring them
back pinching the shoulder blades together and finishing parallel with, and just behind, the shoulder itself. This encourages retraction, switches on the posterior delt (back bit of shoulder) and is generally a better exercise. Also make sure you aren't squeezing your upper traps hard.
Ant
