Can my diet upset my breastfed baby's tummy?

No. Mom's food choices should not upset her breastfed baby's tummy. However, if mom suspects that a particular food or drink causes fussiness or tummy symptoms in the baby, then mom can avoid that food/drink for 2 weeks and see if the baby is happier. If the baby is happier, then mom can resume that food/drink to see if the baby gets fussy again. If fussier again, then maybe there is a connection.
Yes. The foods that you eat ultimately make up the components of your breast milk. In most cases, regardless of what you eat, the breast milk will not upset your infant. Occasionally, foods that might upset your belly or make you gassy can make the infant gassy. Even more rarely, certain foods can cause a more significant reaction in your infant. In general, eat healthy and your infant will be fine.
Yes. While not every baby reacts to foods mom eats in the same way, there are some notorious foods that can cause fussiness: cabbage (which includes sauerkraut, cole slaw, and egg rolls), spicy foods, caffeine, onions and garlic, certain vegetables like broccoli, cauliflower, carrots and asparagus, and large amounts of dairy or tomatoes. Some babies react to small amounts of alcohol too.