Of course, you should read the documents. Some documents may refer to your COBRA rights, 401K information, employer property turnover, etc.. These documents may be harmless. Others may be of greater concern. For instance, employers may try to sneak in a release of liability and $0 severance pay.
If you don't want to sign them immediately, ask the employer for time to review the documents. You can always walk out without signing, reading, or taking the documents. However, it doesn't make sense to do this.
This is an interesting question. I would agree with everything the other attorney said. However, I would need to know the exact documents you are being asked to sign to give any meaningful answer. Obviously, depending on the document, signing it could potentially have different consequences. For example, a release may be fine for one person but not for another, depending on what it contains and if the person being asked to sign it has any known potential claims against the company.
I absolutely disagree that signing anything on the spot will benefit you. If it is a legitimate offer, they should have no objection to giving you time to think about it. Tell them you would like to take the papers home and look them over. Say that you are in no state of mind to sign anything.