What is the meaning of "بدرًا من قابل" (a full moon from next [year/time]) and "قعدوا على أثقالهم" (they sat upon their heavy loads/baggage)? And does "قعدوا" (they sat) mean they sat down or they stood up? And how did the Prophet, peace and blessings be upon him, know that their sitting upon their heavy loads meant their departure, and upon their horses meant their dismounting?

The meaning of "Your appointed time is Badr next year" is to set a date for a future battle in the following year in the region of Badr, which witnessed the Great Battle of Badr.

As for the meaning of "they sat," it refers to their sitting on their camels or horses. The Messenger of Allah, peace and blessings be upon him, deduced their destination from the way they sat: if they sat on their heavy baggage and led their horses aside, they were going to Mecca; and if they sat on their horses, they intended to raid Medina. Camels are typically used for travel, and horses for raiding or racing.