I bought a packet of coconut cookies this morning only to find that milk was an ingredient. I ate them anyway. For lunch, I ordered a veg sandwich, but the chef applied butter on it. Is full veganism practically possible?
I'm sorry this happened to you, but know that you are not alone. I think full veganism is practically possible, but it can take some time, so just keep on keeping on. Every time you don't consume something from animals, it's a win. So give yourself a break and try not to give up. I made plenty of mistakes along the way, but I choose to treat them as learning experiences.
Early on in my veganism journey, I also had a buttered roll, so now when I dine out, I typically ask about the possible situations that could result in my consuming something I don't want to consume. Yes, it can be tricky, and I usually ask only when the restaurant isn't busy. If it is busy, I just won't get the sandwich/burger that might come with the buttered roll, or I'll get the veggie burger without the bun. Lots of people do that to avoid carbs, so it's not a weird or unusual request.
RE: the cookies. I also learned that reading labels before you buy is key to trying to avoid offending ingredients. Plus, I'm lactose-intolerant, so I am always on the lookout for milk and milk-related ingredients, like whey powder. It might seem like a pain to have to read labels, but after a while it becomes second nature.
Veganism does take some effort at first, but when I think about the animals, and how they suffer in both meat and dairy production, it's a no-brainer to do whatever I can to not contribute to the cruelty.