Are corporations people?

For the First Amendment, yes.

For the Sixth?  I'll let you decide after this question and answer from Justice Alito:

JUSTICE ALITO: Do we assume for purposes of this case that your client, a corporation, has a Sixth Amendment right to a jury trial?

 

MR. PHILLIPS: I think the language of the Sixth Amendment couldn't be clearer, that it says in all criminal prosecutions the -- the accused is entitled to a jury trial, and all -- and you know, Article III, section 2, says in all jury trial -- in criminal prosecutions there's a jury trial. So there is no effort whatsoever to limit the -- the individual, or in any way to -- the person or persons or entities that are entitled to those rights.

 

JUSTICE ALITO: What are the peers of the Southern Union Company that would sit on the jury, other railroads?