I've never been successful at re-installing the engine and transmission as a unit. Just my experience, your mileage may vary.
My son and I spent a couple hours trying to do that on my 69, and that was with all of the front-end sheet metal off the car. We gave up and split them, installed the tranny first then the engine --- took a grand total of about 30 minutes for both.
Make sure you support the rear of the engine and the front of the transmission before you split them, once you do there'll be nothing supporting either one at those points otherwise.
Yes, you can install headers with the engine in the car. The trick is to remove the long motor mount bolt on the passenger side first, use a floor jack to lift that side of the engine and tilt it over to get some room, then install that header (from the top). Lower, re-install the bolt, then lather-rinse-repeat for the drivers side. Tip: replace the end bolts with studs. This way if you ever have to R&R the header or even just loosen it to get room to work on something else, you'll have something to "hang" it on during reinstallation which will make getting the rest of the bolts started MUCH easier.