Cooked shrimp keep 2 days but firm up considerably on reheating. Better to prep the slaw, avocado and tortillas ahead and cook the shrimp fresh — it takes 4 minutes.
Frozen, almost always. Most 'fresh' shrimp at the counter was previously frozen and thawed at an unknown time. Frozen thaws under cold running water in 10 minutes.
For tacos, yes. Tails look good on a platter but are a nuisance inside a folded tortilla.
Moderate — roughly a jalapeño, which is what it is, smoked and dried. The adobo sauce it's packed in is milder than the pepper itself.