With only three buttons your options are:
1. use one button for each setting (do you really need a 'normal' alarm?) and cycle through the whole range, saving after you have released the button for say two seconds.
2. use one button for 'up', one for 'down' and one to save the setting, then moving on to the next setting.
3. use one button to call a menu, two for up/down on the menu then the first button to select an option then follow idea 2.
Your problem is knowing which setting you are adjusting and what you are setting it to, for that you need some kind of display, LED, OLED or LCD. Which do you have in mind?
I would use raw ADC readings to do all the calculations and comparisons and only convert to human readable numbers for displaying them.
Brian.