Are Loss Prevention staff authorized to harass, intimidate, and make threats until you sign a statement that makes you confess to stealing when you didn't have the intent of doing so?
Are they allowed to? Well that has two answers.
Does the store allow such actions would be one. the answer is probably not
The law would apply to other question. Depending on what was said and/or done and state laws would have your answers. Talk to a Civil law Attorney as based on your other posts you might have cause for Civil action