My baby is very jittery and frequently makes sudden, quick movements. Is this normal for an infant?

Yes. This is sounds normal (especially if it is intermittent & not constant). Your baby's central nervous system is not fully mature, and it is common for her to make short, jerky movements in response to sudden or loud noises. Most babies have a prominent "moro" reflex (a normal newborn "startle" reflex) that lasts up to 6 months of age. If persistent or severe (full body shaking) consult your doctor.
Yes. Yes. Infants outgrow this behavior around 6-9 months of age. This is part of their normal neurologic maturation.