As a mom of a six year old,I totally can relate.My dd also has a large appetite.
here whats worked for me:
I try not to bring junk stuff home from groceries.
Then I stuff the pantry/fridge with healthy choices.
Once in a while,I make treats at home with whole grains and high proteins.
Usually dd won't eat breakfast,no snack time at school,so by lunch time she is ravenous.sometimes she doesn't like lunch at school,so comes home very hungry and in bad mood,then pigs out on everything.Once I figured this out,I forced her to eat her bf,at first she protested,but now this has become a routine.also I tell her stuff like eating beets gives you rosy cheeks,drinking milk is good for pearly white teeth and eating apples make your skin glow etc.she usually falls for that.
If she is too hungry,try giving her a soup/salad/veggie platter with cheese etc before dinner to fill her up.some creative marketing is needed here.
dd loves princesses,so I say things like"Guess what Rapunzel had today for lunch?" Once she is old enough to understand more about healthy choices,I plan on educating her more.

as for table manners,I would use some humor and work at one skill at a time.maybe you can make a game of it.Who opens their mouth first while chewing loses points etc.
And have a little non-food reward when she masters it.remember she is too little to do everything perfectly at this age,it takes time and practice.
I have to constantly remind dd not to stuff more than she can chew,I think this is bcoz she wants to finish business so sha can play.and then she starts gagging.we are working on it.

no matter what you do,pls do not say things like you are too fat,eat too much,or compare her to other thin girls or say harsh things that would hurt her self-esteem.that wound can last a lifetime! they are so impressionable.

have you tried backyard veg garden?or take her to the store(like a fresh farm market and ask her to pick up stuff)that would normally make them get interested in eating healthy.
Its a lot of hardwork,but worth it,best of luck!