Thank you for participating in the forum AndroidPIT !! We split:
1. As far as the alarm, I'm sorry but I'm afraid there is no solution. He thinks that it is a computer, and when turned off, it turns off completely. You have to have it connected all night if you wish the alarm sounds, or you can also put in "airplane mode", in this case, uses less battery and sound anyway.
2. Note or task alarm: Pretty simple. Use the Calendar. You have it in your applications menu. Select the day and in the menu you can choose whether you want the alarm to sound or not. Furthermore you can sync your Samsung to your computer calendar, so you can have it in both places. To synchronize you need to download the Samsung Kies program.
For now that's the only thing where I can help I can offer other assumptions. For example, I think we need to synchronize the program I've mentioned. As to your last question, I honestly do not know why that is. Forum hope someone can help you.