DD3.5 has started to ask questions about death, how should we approach them? For example yesterday she asked my mom if she is old, she said yes (compared to her, she is only 59), immediately DD asked if she is going to die. I do not know where she got it from, she used a non-english word for death so she could not even get it from her friends. She also stopped eating meat and fish. She has seen my mom cooking fish and was really worried if the fish was still hurting.

I never thought I would have a 3 year old vegetarian.

I would be honest, and tell her that death is a consequence of life, etc. Here are some other threads on the topic, which I hope are helpful.

Regarding the eating, I think it's a tough situation. I think children should exercise some control over what they eat so that good eating habits can be developed. On the other hand, I think some amount of fish or animal protein is a good thing to have in a child's diet. If you're not okay with her being a complete vegetarian right now, I would do my best to reassure her that the fish is really dead when it's cooked, and maybe open up a discussion of suffering and how fish simply aren't as advanced as we are, so we can guess that they can't suffer as much.

I had a backwoods country friend, the kind that puts hot dogs in a deep-fryer, bless her heart. And her three year old would not eat anything besides corn. Her pediatrician just told her mother all can do is offer her food, you can't make her eat. I'm an occasional vegetarian, which means I make the most delicious side dishes when I'm not being a vegetarian. Would you believe this little three year old that wouldn't eat nothing bu corn would eat my brussel sprouts and egg plants.
My husband, who was raised in Texas (I'm a transplant) would only eat beans and rice as a kid because down here they think if you don't have a slab of steak hanging off the edge of your plate it's not a healthy dinner. His pediatrician told his mother it was because he was too lazy to chew beef.

So, there's two stories of children who were just natural-born vegetarians. The hubby is like me, an on-again off-again vegetarian, mostly for convenience. You should try some of the vegetarian hot dogs (boiled, not fried). And here's a link with international vegetarian recipes.
http://www.ivu.org/

And if you do like fried try whipping egg whites, dip thin sliced veggies in them, then fry. (instead of breadi g) If you're using something wet like eggplant or squash put a little salt on the raw veggies and let them sit for 30 minutes before dipping and frying. I never made it to full vegan. I just used to didn't eat stuff that ever had eyeballs.

Oh, and my dad's nowhere close to vegetarian, but he likes boneless meat only because he just doesn't want to be reminded that it came from an animal.

We had this discussion with DS5 for the first time when he was about 3 and asked what happens when someone dies, and where they go, and if Daddy died would he get a new one. It caught me off guard, but made sense in retrospect because we had been discussing the death of DH father with friends and DS was in the listening zone. We went with this - living things don't last forever, their bodies stop working as well as they get older, and eventually they stop working and then they die. that means we don't see them any more, and we can't talk to them, but we can think of them, and talk about them and remember how much we loved them, etc. he was ok with this. and we haven't had any events that brought this up for in depth discussion again.

about the vegetarianism, DS hasn't expressed any concern about eating animals yet...

We've dealt with this to some extent. DD (2 years old) was very curious the other day if the eggs she was going to eat had babies inside of them because she didn't want to eat babies (we assured her they did not have babies). She also knows that eggs come from chickens and has asked if the eggs hurt the chicken when we eat them (ironically she has no problem eating chicken itself...).

We also have discussed death at least in respect to extinction because she is constantly afraid that T-Rex is going to come and eat her. We basically said that T-Rex went to sleep and never woke up again and now he only exists at museums and in books (and that he's stuck in books and can't come out).

Also in regards to meat she's very concerned about other animals eating her so I *think* she gets that we eat animals but just not that we're the predators. We've also discussed the difference between carnivores/omnivores/herbivores and somehow she's decided that the herbivores=good and carnivores=bad (we never implied that). So basically she's still a pretty confused child at this point.