What are the goals of this program? The goals of this program are to help you work out efficiently even at home, with minimal equipment within minimal space!
How heavy should the dumbbells be? I recommend using around 15-25 pounds! But you can always start with a weight you're comfortable with then work your way up.
Is it alright if this is done everyday? Sure, but you can always alternate between your days to equally distribute the work to your whole body for a more consistent form!
How do I know when to increase or decrease the weight I use? You'll know when to increase if the reps are becoming too easy and aren't putting any pressure on your muscles. You can then decrease the weight if you feel that you can't complete the whole workout and within a few reps you're already reaching your limit.
If I don't have dumbbells, can I replace the weight with an alternative, like kettlebells or a barbell? Of course! The best workout is one that you finish. You can even do weighted water bottles as a substitute.
What modifications can I do to this workout if I wanna make it easier/harder? To make the workout easier, you can always decrease the weight and the reps. To increase the difficulty, you can increase the weight you're using and add more resistance to your workouts like adding in resistance bands and using an exercise ball!