first of all, not all of us dump - I've read about 30% do. I've never seen an actual percentage in peer-reviewed literature, but just based on anecdotal evidence (I've been hanging out on bariatric forums for 5 or 6 years), that 30% sounds about right.
I can handle sugar - but high-fat meals I can't. I don't dump, but it just makes me feel like crap.
"good" fats are things like nuts and nut products, avocados, olive oil
"bad" fats are saturated fats and transfats. Saturated fats are mostly animal fats (although palm and coconut oils are also saturated, but evidently not as bad as the animal fats). The saturated fat issue is a bit controversial. They used to say to really limit them, but now some doctors and dietitians are saying they're not as bad as we once thought. I usually go for lean stuff when I'm eating animal products (like chicken, turkey, and fish), though, just in case.