Simply put, you do what you want to, but no way would I use a grapple to load a burning brush pile. Too much stuff catches in a grapple that you would think would have no way of doing so. I'll include a straight rake handle in that category. Don't ask me how I know.
Safety first, and don't even think about having a water hose to put out the fire on your tractor if the unthinkable happens. All you're going to do is spread an oil fire if you use water on it. The water is fine to control the brush fire, not a tractor fire. Since the average person doesn't have foaming equipment or a large enough B/C extinguisher to put out that magnitude fire, the best option is to avoid the risk. Fire is a hungry beast with bad manners.
You have the right idea. Keep the fire small and controllable. I've burned an enormous pile of brush by just feeding it slowly into a relatively small fire. Burn when it's cold, and with the least wind possible, and preferrably, as shortly after a rain as possible. Make 'storage' or staging piles that you can push onto the embers (assuming you have enough time) after the first lot burns down. You can keep moving and sorting with your grapple into those piles while the main pile burns but go grab the bucket and use a skim technique to push the new piles on top of the embers. The bucket will clear the hot coals out of the way (and any nails you might miss) and will also keep a lot of heat off the front of your tractor. Remember, that fan's gonna suck every bit of that heat through the radiator and fan the flames if something ignites. Even if the grill on your tractor is not plastic, you could still wind up doing some serious damage to the radiator with that much heat. Just stay back from it until it burns down. and approach low with the bucket. Once you get the pile pushed in close, you can lift and curl forward to roll it onto the embers. You don't have to lift high, and it's better if you don't. Keep that bucket between your tractor and that fire. It's the best armor you have.
Like so many others have said, make sure you have an escape plan and that NOTHING compromises it. A second person for a watch is a stupendous idea. I doused a pile of mulched leaves that I was silly enough to set on fire. I hosed them with water for at least 30 minutes. I checked them the next morning before I left for work, yep stone cold. I thought. My new neighbor called me about two hours later to see if I was home and to let me know the pile was smoldering again. He and I have been good friends since.
Murphy's Law #2: If it can go wrong, it will, and at the least opportune moment. Murphy's Law #1: Don't mess with Mrs. Murphy.