Hi, I'm 25 and had a PE as well 6 months ago... They five you Heprin to help try to dissolve the blood clot, and Coumadin to keep the blood thin so prevent future clots, and to help the body naturally dissolve the clot on it's own..
The time it takes varies, but could be weeks, or months.. When you are first on Coumadin and have recently taken Heprin, they have to check the blood every 6-12 hours (varies) to check to make sure it's not too thin, etc.. So yes the constant blood work is normal..
As for after the hospital, if the clot was surgery related, he'll probably be on Coumadin for 6 months.. He'll probably have blood work twice a week, then once a week, then usually every 2 weeks to check INR (Thickness and clotting times)....
I hope this info has helped.. Best wishes for a speedy recovery!