You should not use the "R" with the circle around it unless the mark is federally registered. Also, don't confuse trademark registration with copyright registration. An artistic design might better be protected via copyright registration, depending on how it is being used.
Anybody who is charged with a crime in entitled to a fair trial and "due process." If important evidence was somehow hidden that could have helped you, a Court of Appeals would want to know about that in a timely fashion.
They can request her to take the test. However the portable machines are not very realiable. If the only evidence is the portable machine results, they have a weak case. I will still suggest you hire a lawyer.
Who did he ask? Who is "they?" Some states have minimum household income criteria for a "free" lawyer. I will tell you that the primary issue in extradition is "identity." Is this person the person who the other state is asking for. If so, he can probably be extradited. Also, if the state eventually punishes him, he will almost always get credit for time he sat in jail waiting for extradition.