Criminal attorney here to agree with Amelie06. Miranda is only for custody + interrogation. They don't have to be read if the police aren't both holding and questioning you, and a failure to read them in that case would lead only to the prosecution not being allowed to use the statement as part of their main case.
Also, Alicia learned the charges when Cary was being arraigned. Arraignment was the moment at which Cary was formally charged and when he had to be told the charges against him. In most places in the country, you can be held for 48 hours without being charged. Also, the prosecutor determines the ultimate charge, not the police.
And discovery would never occur at such an early stage. The US Constitution provides no right to discovery. I'm not sure how much Illinois requires, but the state's attorney wouldn't be required to turn over information that soon after an arrest. Realistically, the police haven't even finished their paperwork yet.
This show generally gets the criminal procedure correct. For instance, that much bail in a drug case is *of course* going to be subject to an examination of its source. (I can't remember whether the defendant has to prove the money came from clean sources or the prosecution has to prove it didn't, but it's a lower standard than beyond a reasonable doubt, so it's not the equivalent of being able to convict Rojas of a crime.)
The conflict of interest was poorly handled, though. Bishop and Cary would both have to waive privilege, and if they did, it would be a much bigger deal for the judge to disqualify Alicia anyway. There is a strong right to choose your lawyer, as long as you can afford whomever you want.