Welcome to the wonderful world of Turbo Buick ownership and upgrading. It sounds like your car may indeed be testing you to see how you behave. I firmly believe that these cars have a heart and a soul. If you treat them right, they'll treat you right. They are constantly testing you. All three of my cars (2 previous to my current) really tested me over the years, but I still love em. Once they are in your blood, you never loose the passion. My advice, don't get mad and start cussing her or throwing stuff, just keep your cool, take a lot of breaks, for this is a test. Heck, even this past Tuesday night I went rounds with my car Sarah, removing some simple bolts and a bracket for my stock location IC. A simple job that should have taken me no more than 10 minutes, wound up taking almost 2 hours.

I just kept my cool and took breaks and kept at it. You definitely have to have a lot of patience when working on these 20+ year old cars, but you just have to keep telling yourself, it will be worth it in the end. Anything worth doing, will require a lot of patience and persistence. I feel your pain. A torch should loosen the nuts/studs so you can get the turbo off. Use caution when removing the oil drain line as we don't want to move it much, or else it could become kinked and or cracked, leading to a massive oil leak large enough to set off alarms at your local EPA office.
Quick, save the ducks!!!
I've seen some new bolt extractor tools advertised recently that show some promise for getting your broken dp bolts out. Once you get that issue straight, don't forget to use anti seeze on the bolts and don't tighten each one down until you have them all started. The bolt holes in the dp flange have enough play in them that you can move the downpipe around slightly in order to line up the bolts. Once you have all 4 bolts started, position the pipe so that it clears surrounding items, then while holding the pipe, tighten each bolt. Cake from there on out. One other tip, when you go to re-install the turbo, if your oil drain gasket is intact, you can get away with cleaning it up, and re-sealing it with copper high temp silicone. If not, most of the turbo vendors can supply you with a replacement. Use just enough silicone so that excess doesn't drip into the lifter valley via the oil drain tube and clog up a lifter. I always install the oil drain tube first before installing the turbo, but either having someone support the turbo, or let the turbo rest on the header without it being fully seated. Some have had great luck with replacing the factory 2 bolts with studs and nuts. I can see where this would make installing the oil drain a whole lot easier. Also, make sure your 3 bolts are tight and install a new 3-bolt gasket with high temp copper silicone if your car does not have one already. I've had those 3 bolts come loose a few weeks after installing the turbo on me in the past, so make sure they're tight. Check really good for leaks before going out for a test drive.
Try not to get discouraged, hang in there and we're all here for you.
You're car will love you for your patience and TLC.
Just remember,
How would Tennessee treat Herbie?
Patrick