If you do want to take a taxi, it is a fixed fee of €30 from the center (a large defined area which includes the Prado), and no tipping is required beyond this. I'd leave at 5 PM for that 7:30 AM flight; at that early hour, the ride to the airport shouldn't be impeded by traffic.
If you want to take the bus, at that hour it goes from Plaza de la Cibeles (near the Prado), not from Atocha station. It's €5 per person, and at that hour runs every 35 minutes. Here are details from the official website; scroll down to "Línea Exprés (line 203)": http://www.aena.es/en/madrid-barajas-airport/city-buses.html
The train from Atocha doesn't leave until 6:02 AM; I would feel that is too tight for a 7:30 departure, as Madrid's airport is huge, so just getting to the airport train station could still mean lots more time getting to your check in (LOTS more if you are not leaving from Terminal 4, where the train goes). The website does say that during the closure of Metro line 8 (maybe that's the closure you read about), the train from Atocha is running more often. Details here: http://www.aena.es/en/madrid-barajas-airport/train.html
Note that terminals 1, 2, and 3 are connected, and terminal 4 and 4S are connected, but these two "complexes" are separate from each other. Be sure you know where your departure is from to avoid wasting time.