The taxes should be pro rated from Jan. 1 until the day you closed the deal on the home you sold, and that would have been deducted from your proceeds on the HUD-1 closing statement. On your new home, you should get taxed from the day you closed until the end of the year.
Some courthouses don't update their records very often. I gotten MANY calls from sellers who got another tax bill for their old home from the previous year. It's a mistake, and you may have to go to the assessor's office and have them forward the bill to the new owners.
Regarding the suits - as a Realtor, I asked many clients my first year, "would you rather have your agent show up in a suit and tie, or in casual clothes like Bob Vila, with a tape measure and a flashlight on his belt, ready to crawl into an attic or under a crawl space?" They ALL preferred the latter, and since that's how my broker / owner dressed, I did too. I wore the suit for my photo, and that's it. For closings, I'd wear dress pants and a dress shirt, but suits are over-rated, although they do have their place and time.