The clock that runs your day, in one screen. Property-carrying drivers, 49 CFR 395. Memorize the numbers, understand the exceptions, log honestly.
Off-duty driving of the truck for your own purposes. The classic use: a shipper or receiver runs you out of hours and you move to the nearest safe place to park. Log it as PC with a note. It cannot be used to advance a load, and "nearest safe spot" means nearest, not the truck stop 90 miles toward home.
Source: FMCSA, Personal conveyance
FMCSA is running two pilot programs: a Flexible Sleeper Berth pilot that adds 6/4 and 5/5 splits, and a Split Duty Period pilot that lets you pause the 14-hour window for up to 3 hours of certain off-duty time. They are pilots, not rules; unless your carrier is enrolled, the numbers above are the law.
Source: FMCSA, Hours of Service
Say no in writing and read the coercion rule. A dispatcher who says "just fix the log" is asking you to put your CDL on the line for his schedule.