First issue. Weak brakes. Check your linkage. Turn the black thumbscrew on the brake linkage in so that it gives more braking force. That's the usual culprit. If that doesn't help, check to make sure the brake arm is indeed moving the caliper. Check the condition of your brake pads and also check the brake disc.
Now, for your stalling. I would check the idle. And make sure when you check it, you're checking it with the brakes fully applied. It's possible that if you're checking it at neutral trigger, your throttle trim is actually holding the carb open rather than the idle stop. You have to make sure the idle stop is what is actually holding the carb open. If it's not that, check for binding in the drivetrain especially with the clutch, clutchbell and spur. If the clutch is spent, the drivetrain will lock up and stall the engine whenever you brake. But I'm more inclined to think it's your idle.