The reason you need to keep taking vitamins is because breastfeeding takes a lot from your body. You need them for YOU.
Its always good to take a multivitamin, it just insures that your body is getting enough nutrients, i am going to assume that like during pregnancy, your body directs nutrients to baby, and to your milk, so it is important to replenish those nutrients so baby gets more as well. As far as milk production goes, i pump too. Pumping is not as effective as regular breastfeeding, but since i cant breastfeed i dont have very much milk and have to resort to formula sometimes.
Eating oatmeal and carrots. Drinking at least 64oz of water/hydrating liquids, there is a vitamin called fenugreek you can take, mothers milk tea etc. Also investing in a good pump and pumping both breasts at a time. It helps to relax and live a low stress lifestyle.
Thank you very much :) for your advice it really helped me a lot.