How to replace eggs
Flaxseed: Grind flaxseed until you have flax meal. One egg in baking equals 1 tablespoon of ground flaxseed mixed with 3 tablespoons of water. Set for 15 minutes. It will turn into a gooey texture and will act as a binder.
Banana: 1/2 mashed banana corresponds to one egg.
Apple sauce: 60g for one egg.
Silken tofu: You need ~65g of silken tofu to replace one egg.
Aquafaba: When you open a can of chickpeas next time, keep the liquid left over! Whisk it with a hand mixer for 3-6 minutes to get to semi-firm peaks. You will get the perfect egg white replacement. You can even make chocolate mousse, meringue, or vegan mayonnaise with it.
How to replace dairy
Butter: You can always use margarine to replace butter. But there are also great vegan butter alternatives, which are in no way inferior in taste to those made from cow's milk.
(Whipped) Cream: The same applies to cream. But not all of these products can be whipped well. But here's a trick: chill a can of coconut milk or coconut cream in the fridge overnight. Scoop out the hardened cream into a bowl. Whip with a mixer until its light and fluffy peaks form. You can also add vanilla or some happy maple syrup for flavoring.
Buttermilk: mix 240g of your favorite soy or unsweetened almond milk with 1 tablespoon of vinegar (cider or white wine vinegar, lemon juice works as well). Combine milk and vinegar, and whisk together. Let sit for 5-10 minutes to thicken and curdle.
