for your 1st question:
usually by the time baby is 6 months, just milk alone won't give baby all the nutrients that he needs. iron is one such example. most rice cereals are fortified with iron because by 6 months, baby need to get more iron to produce blood. it's ok to mix the cereal with water, it will just taste more bland. when i was weaning my baby, i mixed with milk because when i mix with water, he refuse to eat it. and after his cereal feed, i will feed him milk. if you're feeding 4 tbs of cereal, it sounds ok to me... it's a lot.. when my baby was 6 months, he was only eating 1tbs of cereal.
for question 2:
as long as baby has passed allergy test, it is ok to introduce that vegetable to other meals. just make sure you only introduce one new food at a time. so if you're introducing fruits, dont't introduce a new vegetable at the same time but it's ok to feed the other vegetables that already passed the allergy test. if you wanna play safe, then just introduce the new vege or fruit without the others. but at some point in your baby's life, she'd need the variety for good taste and nutrients.
you might want to invest in this book that i am using. it's called "feed your child right". it's written especially for asian parents. i'm using that book now. it's pretty useful.