No you do not, the big two are flossing and brushing. If you want to use mouthwash as a tool in your oral hygiene arsenal that is perfectly okay, but it is not a substitute for brushing and/or flossing your teeth.
Fluoride helps to strengthen the enamel to prevent the development of cavities. Especially if you have a very acidic diet, it’s important to make your teeth stronger to prevent tooth decay.
You can whiten your teeth as often as you’d like, the main limitation is how prone you are to sensitivity. If they’re sensitive you may want to wait a couple days/weeks in between sessions. Likewise, you can whiten day after day until the desired shade is achieved if your teeth are up for it.
Babies are born “perfect,” in the sense that they aren’t born with cavities/cavity causing bacteria. However, it is frighteningly easy to introduce irreversible bacteria to babies without consciously doing so. For example, a caretaker, (mom, grandma, grandpa, sister), may sample a baby’s food with a spoon then proceed to feed the baby with the same spoon. By doing this, all the foreign and potentially harmful bacteria from that individual’s mouth, (such as periodontitis and Streptococcus mutans), will then enter and infect the baby’s mouth; which could lead to health problems as the baby ages.
Some common ways to transfer bacteria from one individual to a baby aside from kissing include but are not limited to: blowing on their food, sharing utensils/cups, and licking a pacifier to “clean” it.
Similarly, it is recommended to avoid having individuals kiss the baby’s face, (grandparents tend to hate this one). The transfer of oral disease is commonly seen from this, such as Herpes Labialis (HSV-1) and Herpes virus Type 2 (HSV-2). Both of which are currently incurable.
To summarize, avoid the transfer of saliva from someone else to the baby in any regard and do not allow people to kiss your baby’s face. However, as with most pieces of advice, these are simply recommendations and it is up to the parent(s) to do as they see fit.
Unless your sport is golf, swimming, track and field, cross country or a sport along those lines, you should wear a mouthguard. A mouthguard is the definition of "better to have it and not need it, than to need it and not have it." It's a very simple appliance that not only protects your teeth from getting wrecked, but it can also reduce the trauma you experience with a head injury.