Extra virgin olive oil is great. You need fats in order to carry fat-soluble toxins out of your body, and you need them to keep your brain and other organs functioning. The other things you used to prepare your roasted broccoli are fine, too.
The mucus could be die-off, since garlic is antifungal. It could also be a type of reflux. I drink water when I’m thirsty. I honestly believe the harm caused by dehydration merits more concern than worrying about diluting your stomach acid.
Skip the butter. Be careful with coconut products as you introduce them, to make sure you don’t plummet yourself into intense die-off. Eat gradually more as you learn your limits. Celery and zucchini are totally fine.