I do agree that the questions you provided above aren't truly relevant questions because the purse had nothing to do with Caylee's body, the crime scene wasn't a frequently traveled place during the summer, the shovel showed it had nothing to do with a crime, etc.
But, my question was in regards to the tape, the tape that was found with Caylee's body. If she did use that tape prior to death, after death, to apply to Caylee's mouth/nose.... why would she leave such incriminating evidence behind in her house. And, where was this tape kept... In GA's locked shed or in his garage. And finally, what luck GA happened to have to stumble upon this roll of duct tape and proceed to use it throughout the time of investigation until it is completely gone. No way to trace the tape to anything. Casey must've had a great plan going for her dad to grab the murder weapon and use it up before LE found out.
It would've been a heck of a lot worse for Casey if she took the duct tape and left it in her car!! In that case, when they found the body and noted that the duct tape found in her car, as you had suggested she should've put it, matched the duct tape found at the crime scene it looks especially bad!!
Duct tape is not a commonly used murder weapon like a knife - it's a household handyman item!! No need to dispose of it, although in a perfect crime she would have. But there were many stupid things she did....among them - try not to act so happy by partying it up in the immediate days after your child goes missing or "drowns in a pool accident".
George using the duct tape to hang flyers was merely a quirk of this case - how was anyone to know that they would find duct tape on a body at some time in the future?!