Yes is the answer. Vitamins dissolve in blood and the required amount is absorbed by the body. The remaining excess vitamins are excreted by the kidney which turns the urine yellow.
The multivitamins you took probably has a lot of Vitamin C (Ascorbic Acid) in it. This vitamin is known to cause very yellow/orange urine. I have experienced this myself.
It certainly can. Since you just started taking a multi-vitamin, check the label on the bottle and see if it contains B vitamins or B-complex vitamin. These can turn your urine bright yellow.
Taking a multi-vitamin can make your urine more yellow as you would excrete the excess vitamins back into your urine. Dehydration is another cause so as long as you're drinking the same amount of liquid everything should be fine.