If there’s a warrant for someone’s arrest. If they go with an attorney to turn themselves in. Will that person so straight to court?

Surrendering with an attorney has some advantages, the most important of which is that once you're represented by counsel, the police should NOT interview you without your lawyer present. As far as going straight to Court, the police will still have to process you (fingerprint, get your pedigree information, etc.) however, many times if you're represented by an attorney they can speak with the detective to arrange a beneficial time for you when the detective is not otherwise busy that may result in a reduced processing time and get you out more quickly.