I am a highly paid salaried employee in Arizona, and am required to travel for trade shows which might include Saturday and Sundays. Is my employer required to give me comp time off? I am expected to work right thru the following week, without ANY time off-- thur 12 straight days. Is this legal?

Yes, it is legal.

While an exempt employee MAY be given comp time (non-exempt employees may not) it is not required by law. It is up to the employer whether to offer comp time or not.

I thought there was some kind of law that an employer cannot make an employee work more than 5 straight days in a row (or 40 hours), without some kind of mandatory time off.

No, there is no such law in Arizona.

This is really a new subject, but I don't know how to begin a "new thread". Anyway, my 17 yr old son is employed by a local pizza place in Arizona and get's random paychecks, once every 2 weeks, or 3 weeks, or now it has been 23 days! Also, there is no record of what dates the paychecks cover, hours work, rate of pay, or taxes deducted. Just one lump sum. Is this legal? I have contacted the manager and asked for a reconciliation since I am his mother and my son is a minor and I feel I need to get involved. However, to date I have not received any documentation. What can I do?

See here for information on paydays in Arizona. The employer must have a defined payday and it must be at least semi-monthly, no later than 5 days after the pay period ends.
http://www.ica.state.az.us/Labor/lalawfaq.htm#Q1

My sources say that Arizona only requires a statement of deductions and earnings for exempt employees; doesn't make sense, but it appears that is the law.

And if I may offer some other advice, you stay out of it. Your son may be a minor, but he is the employee and you have no legal standing in this issue. At 17, he is old even to start fighting his own battles. The state will take his claim directly from him. I managed the payroll for a large nationwide company that hired many employees under 18 and there was nothing that made us less likely to try to help an employee when mom or dad called instead of the employee. You can give him advice, but he needs to handle this.