Yes, access to a fair trial is limited by the Civil Procedure Rules, because not all of the information can be presented to the court. The most common problem is the hearsay rule. Sometimes it's very important to be able to say what someone else said. Sometimes it's impossible or inconvenient to offer the person as an actual witness, and then relevant evidence is excluded.
The access to a fair trial is not limited by the Civil Procedure Rules. The Civil Procedure Rules were put in place and were designed to improve access to justice by making legal proceedings cheaper, quicker, and easier to understand for non-lawyers. This has no impact on a fair trial.
Civil Procedure Rules don't hurt a person's access to a fair trial. In many cases, these procedures help a person receive the fairest trial possible. Most people don't realize how useful the Civil Procedure Rules are in the American legal system at the moment, and they've worked ever since the start of their implementation.
The Civil Procedure Rules just protect some victims, witnesses and accused. If the victim or witness is a small child that testimony is handled differently. The press isn't allowed into the courtroom during some cases so the jury won't somehow end up hearing something that will sway them in one way or another.
Access to a fair trial is still allowed with the Civil Procedure Rules. You still have to have a trial if you are convicted of a crime, you still get to have a lawyer represent you, all that you need to worry about is if there is a jury or not.