Sure. Mothers in all cultures eat the food native to their countries. I don't think those in mexico, greece, or thailand are eliminating anything from their diet. We know what a mom eats during breastfeeding flavors her milk to help the baby become accustomed to their native food. Some children can be fussy after certain foods, but mom's diet is blamed too much for a baby's fussiness.
Yes. Very few foods need to be avoided during breastfeeding. Current feeling is that eating highly allergenic foods such as nuts and fish during pregnancy or shellfish does not increase the risk of allergies in the baby. Foods containing stimulants such as caffeine can affect the baby. A good rule is that if you see the baby consistently getting fussy after you eat certain foods avoid them.
Yes. One of the benefits of breastfeeding is your baby gets to taste various flavors, unlike formula babies who get the same thing each meal. I think eating what you typically eat acclimates baby to the flavors your family eats, which is great to (hopefully) ward off picky eating. Of course, most preschoolers become picky, but that's another topic!
Yes. Breastfeeding mothers may eat their usual diet, even if that includes spicy foods. If a mother notices her baby having a possible reaction (such as fussiness, sleeplessness, or rash) after the mother had eaten a particular type of food, she can wait a few days and try that food again. If her baby repeats the reaction, then the mother can avoid that particular food, and inform the doctor.
Yes. Babies are exposed to flavors and proteins from the foods you eat, even while you are pregnant. Breast milk is unique to each baby/mother pair. Moms from different cultures eat very different spices in their diet. If, however, you suspect a certain food or spice in your diet may be bothering your baby, try going without it for a week and see if the baby's symptoms resolve.