Drill bit for extracting easy out
 

First one be very carefully, it will be easy to break the bit you want/need to use.
You need a hard material for the hard material (will want to snap off).

I would go buy a (couple) good drill bit from industrial bolt supply (different sizes, starting small).
Talk to the person behind the counter about what you want it for (bring a picture).
How did it break off (pictures)?
Did the break flat or jagged?
Getting the drill bit started and keeping it centered will/can be tough (without breaking it).
It will want to bind and break the bit.
Lets just say I have been there done that a few times (it can get messy real quick).
If you have room to drill a relief on the side it can help (but raises hell with your hole).
Were you using the old school easy outs or one of the newer designs?
The newer designs (IMHO) hold up better (less apt to snap off).

Yes get it looked at by professional do it right the first time this will save you a lot of head aches down the road.

Yes, this option unless there is enough of the broken bolt available to weld a nut to. If you can have someone weld a nut to the remains it will typically spin right out do to the heat of welding expanding the bolt. As it cools it retracts away from the threads thus freeing it up.

This is very true.
If you make to big of a mess and you/they can't clean it up you will have to replace it.
Drilling an easy out is tough, the drill bit's want to get bound up, then they tend to break (adding to the mess).

last time I broke an easyout I was able to use a small punch to back the broken piece out of the hole. For some reason it didnt bit so hard into the screw that it was permanently jammed in there...just remember, it's a reverse thread so you'll want to aim the punch as if to tighten, Come to think of it, it wasnt a punch it was a small drift pin...handy to have a set anyway if you don't. IIRC after removing the broken easyout, I used a larger drill to fit the next size easyout.

Try to use a carbide drill bit by hand and you'll bust it within 20 seconds. I have in a few desperate situations used 1/8" carbide burr bits and a dremel to bore into hardened broken bolts but it takes a very steady hand and good eyes, had enough sense not to snap easy outs so far.

If you can get things apart for the average non mechanic the machine shop suggestion is the best solution as stated for several reasons.

Huh?

You're bolting the outer primary cover back on, and broke off three of the mounting screws?

One? Chit happens.

Two? The universe is sending you a message.

Three? You're not listening.

Maybe I've misunderstood what you're saying here, and if I have, my bad.

But honestly, if you broke off three of those, you're doing something majorly wrong.

Where's this sit now? I'm reading that the outer primary us off, and you've got three broken off screws in the inner primary. Is that right?