Hourly, HOS, Log.

He's exempt from logging. He's not exempt from HOS. (Getting caught is a different subject.)
He still has the 11/14 daily and the 10 hour reset. He also, like in his question, limited by the 70 hour clock.
The only clock he doesn't have to worry about is the 8 hour driving/30 minute break clock.

 

If you are getting compensated, You must log/account for the time regardless of where or who it is for. Part timers can get themselves into hot water and the companies (or a lot of them) turn a blind eye to it... until the crash.

 

Not 100% accurate. If you are working for a motor carrier than even getting paid or not doesn't affect on duty time. Basically any work for a motor carrier, paid or not, is on duty time. On the same token, getting paid doesn't mean one is automatically on duty. Now the other hand, non motor carrier job does require compensation to count as on duty.

 

How old is the equipment you drive?

 

The local short haul exemption doesn't exempt you from going over the 70hrs in 8 days rule. Its only real benefit to you is that you have the option of running a 16 hour day once within that 70 hour cycle (you'd need a 34 before you could use another 16 hour exemption in that cycle).

As @MACK E-6 said, if you satisfy those requirements, you'd be exempt from having to maintain a detailed log. If so, you're recorded punch in and punch out times will satisfy the record of duty status requirements.

In your described scenario, if you pull 70 hours in a Monday through Friday period, you'll require a 34 hour reset to be able to have a fresh duty cycle to begin working, so no, you would not be able to run loads on a Saturday in your scenario. You could however work in the yard, hostling, working freight etc. You'll just require the 34 to begin driving a CMV again.