Are home doppler monitors a good investment?

Not really. Opinions will differ, but with obstetric care, you have open access to your obstetrician, usually for an unlimited number of visits. If you want reassurance of the baby's heartbeat, i'd rather you come in to see me than make yourself nervous with a home monitor. If you do decide to get one, remember that finding the heartbeat, especially early on, is not necessarily easy. Don't go crazy.
Not usually. Most people get nervous if they can't find the heart beat because they dont know how to properly use the monitor.