Is it legal for the police to arrest you without showing the warrant and or reading your rights when booked?

An arrest warrant is not always required. When the police have probable cause to believe that a person has committed a crime, they can make an arrest without a warrant. The exception being the police cannot arrest a person in their own home or private residence without an arrest warrant. The 5th amendment states that citizens shall be protected against unreasonable search and seizure. This ot protection extends to the right of persons to not be arrested in their home without an arrest warrant.

Even then, there are cases where it is legal for the police to enter a private residence to make an arrest without an arrest warrant. For example, when the police are in "hot pursuit" of an individual they suspect has committed a crime and that person enters a private residence. Additionally, the police can also make an arrest without an arrest warrant to protect others from imminent danger, to prevent the destruction of evidence, or when contraband is in "plain view". Finally, people can also be arrested without an arrest warrant for certain traffic related offenses.

When an arrest warrant is required, the arresting officers must show the warrant to the person at the time of arrest or shortly thereafter. The only time an officer does not need to show proof of an arrest warrant is when they reasonably believe that doing so would threaten their safety, the integrity of evidence, or cause the suspect to flee.

As for reading you your rights, the "Miranda warning" need only be given when a suspect is arrested and then questioned. If the subject is only arrested without questioning, then they need not be read their rights. Any questions asked incidental to the booking  process is an exception. So a suspect may be asked their name, address, birth date, etc. without being given their Miranda warning.