Simply, it is the visual language used by the Deaf community in the United States. There are regional dialects of ASL based on different parts of the U.S. and different communities.

And yes, there are signed languages in other countries, i.e., British Sign Language, etc. In fact, there are somewhere between 138 and 300 different types of sign language used throughout the world today.

No. It is a separate, distinct language apart from English and it's common that many ASL signs don't translate perfectly to English, just like in other (spoken) languages.

ASL is a complete, natural language that has the same linguistic properties as spoken languages, with grammar that differs from English.

American Sign Language was originally conceived and designed over 200 years ago by Thomas Hopkins Gallaudet (check out Gallaudet University for more about him). In 1817, Gallaudet established the first national school for the Deaf community in the U.S. in Hartford, Connecticut. But like English and any spoken language, ASL continues to adapt and evolve for those, and by those, who use it.

• ASL is considered as a foreign language
• Sign language is not only a sign, gesture language but also a facial expression language
  Sign Language users often use facial expression to change the meaning of signs.
  For example:
  Lowering eyebrows indicates who-what-where-when-why question.
  Raising eyebrows indicates yes/no question.
• Children acquire sign language in the same way they acquire spoken language
  Through interactions with people around them, deaf babies explore the hand shapes and movements that make up signs by babbling with their hands. In the early developmental stages, deaf children often substitute easier handshapes for more difficult ones.

Assembled from AML-Global Services.

Obviously, these are going to vary from person to person, but here are some ones just from a simple Google search... and check out the video below, from BuzzfeedVideo.

All Deaf people wear hearing aids, and hearing aids restore hearing.
Hearing aids are assistive devices that, at their most basic function, amplify sound. The use of hearing aids is restricted to those who have enough residual hearing to make effective use of them. While many deaf people have some degree of residual hearing, it may not be enough to utilize a hearing aid. Even if it is, a deaf person may choose not to wear one.

The National Institute on Deafness and Other Communication Disorders (NIDCD) provides more in depth information about Hearing Aids, their purpose, functionality and limitations.

All Deaf people read lips.
Speechreading, historically known as lipreading, is not considered an acquirable skill, but rather an inborn talent. Only a small percentage of deaf people are considered expert speechreaders, meaning they may be able to understand 50-75% of what is said. For the rest, word comprehension may be in the realm of 5%-10%; comprehension of the actual subject matter and concepts being presented is often low due to the strain of attempting to decipher words.

All Deaf people use sign language.
Not all Deaf people communicate in the same way. American Sign Language (ASL), Signed English (SEE), speechreading, writing, gesturing, and speaking are all methods of communication which may be utilized by different Deaf people.

All Deaf people are mute.
Never assume that Deaf people cannot speak. Some can, but choose not to; some cannot. Compare this with hearing people and their ability or inability to sing. Some can and choose not to; some cannot. Those Deaf people who do choose to speak will often have an accent, which is sometimes difficult to understand; however, do not shame a Deaf person who chooses to speak by telling her her voice is incomprehensible. Instead, tactfully suggest it will be easier for both of you to communicate by writing until a better communication method is available.

Assembled from Hearing Like Me.com and VAWnet.org.