Not answering your questions in order here, just my thoughts:

(1) I would chose an entirely different chain to shop at. LP travels, so the other two stores of that chain in your area - you may encounter the same LP (actually within an hour radius). Clearing your name with the store - the first question a manager will ask is "why did you not go with the LP guy to the office", followed by "why did you abandon your purchases".

(2) Change your shopping habits to look less suspicious. Don't dig in your pocket or purse. Wear the sweater into the store, not bring it in a bag.

(3) Yes, they can call the police using your License Plate number. Or the photos just may be hanging in the LP office and possibly employee time clock area of all local stores of that chain.

(4) charges - that would be up to the prosecutor based on evidence such as video.