Them not reading you your Miranda rights is not a violation of your Fifth Amendment rights, unless the interrogated you in a custodial setting. But it sounds like they already had the information they needed to arrest you, and had no need to interrogate you.

Police do not have to show you the arrest warrant or search warrant at the time of the search or arrest. The point of a warrant is to put an impartial magistrate between you and possibly-overzealous police officers, and to allow your attorney to contest matters later, if justified.

I do think your Sixth Amendment rights were violated. You have the right to hire your own attorney for any charges against you. If you cannot afford an attorney, they must provide you with an attorney for any charge with the potential of jail time. The crime of failing to pay a fine certainly sounds like a jailable offense, especially since they did put you in jail, if only briefly.