Yes, for a wood or charcoal barbecue, you must let the fire burn down before you can start cooking, usually 15 minutes to an hour.
It will always mean 'earlier'.
Yes, but it means more than that. If you have a second thing that depends on a first thing, finishing the first part before the second part is ready to start is called "finishing in time". Finishing with extra time to spare (well more than the minimum) is called finishing in plenty of time.
"Make sure you light the barbecue in plenty of time"
The coals have to burn for awhile before they are ready for cooking on. So that first part has to be finished (getting the coals ready) before the second part can begin (the cooking). You have to light the barbecue early enough that that process will finish before the intended cooking time arrives. So it means "Make sure you light the barbecue early enough so it definitely has enough time to be ready before the cooking starts.
Will you be in time for lunch? Yes, I will be there in plenty of time.
Yes, I will finish the process of traveling to the location where the lunch is well before the scheduled beginning of the lunch.