The "court" can be the whole building including offices etc. But you can say "the judge sat in number 1 court". "Courtroom" refers to the actual place the case is being heard. "The judge entered the courtroom at 10 am".
I need to go to the court to pay my fine
I live near the courts
The prisoner was brought to court
The courtroom was full
The prisoner sat at the front of the courtroom
The courtroom was dark