Breast feeding is generally recommended for the first 12 months of life. The amount of breast milk taken each day may decrease once solids are introduced (usually around four to six months). Of course, you may stop breast feeding anytime you need and want to, as formulas are available that closely mimic the qualities of breast milk. But cow's milk from the carton just doesn't have the same benefits as breast milk or formula in the first year of life.
Now to answer your second question. Your toddler probably does want to walk, but is just getting up the courage. Toddlers start walking on their own at different times. Some do it before their first birthday, others are older (even a year and a half). If your 16-month-old has been reaching other developmental milestones within the usual range while progressing in the right direction, I would not be alarmed. I suspect it won't be too much longer before you are chasing your toddler all over the house. If not, please discuss this with your baby's doctor at the 18-month checkup.