If you set your feet up correctly then your practice will improve dramatically. However, you cannot isolate what’s happening in your feet from your body any more than you can isolate your head from your shoulders.
1) Toes and heels together is not a good standard. It doesn’t fit everyone’s feet. It actually causes problems for many with hip and spine alignment, and can also challenge your balance. The challenge is to listen to your body, and not just words. In every practice take the words instructors are giving you and move your body so that your asanas make more sense than before. Learn how to notice what each little movement does and make each movement count for improvement in every class and every day.
2) Grip the floor with your toes. Many instructors ask you to plant your toes down. That is naturally going to swing the weight forward somewhat.That extra weighting happens because your body is intuitively trying to stop you from falling forward or sideways. It will not help you though in balancing poses if you have flat feet. In the case of flat feet what helps you is to lift your toes, so the shape of your feet can change and your weight can be evenly balanced.
3) Every little thing you do has an effect because of the connections of the feet into the floor and because the feet are a pathway to the rest of the body. But you are not a body simply stacked up on top of feet. You are a complex arrangement of soft tissue that have incredibly subtle effects with every single degree of movement.