No. The officer would have needed a search warrant to enter your home, but may arrest anyone in the street if they have probable cause to believe they have committed a felony. That's why he coaxed you outside.
Remember that under most circumstances the remedy for an improper arrest is not dismissal or termination of the criminal charge. So even if the arrest were improper, and your description does not persuade me that it was, you would most probably still be facing the original charge.
I agree.. The Deputy would need a search warrant to enter the house. They will routinely knock on doors and try to get you to come outside. I think your legal research is good and you should take a copy of the declaration in support of arrest warrant and show it to an attorney. Good luck! I would not explain anymore circumstances about the rental car or facts of the alleged GTA here.
Outside the home, even on the porch, one does not need a search warrant. Since he didn't enter the home to arrest you it looks valid based upon these facts.
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