"4 alarm" just means 4 fire companies are there. Even if the main blaze is out, there's still smoldering, smoke, and the risk of more small fires breaking out. Meanwhile, LOTS of trained firefighters are needed to enter a building in this condition and rescue people who are trapped or unconscious inside.
Not in any fire department I'm aware of. Fourth alarm is generally 12 to 16 engine companies, plus aerial ladders, rescue units, one or more batallion chiefs, frequently a division chief, and a lot of ancillary gear. With New York's staffing, we're talking close to 200 guys.