Taps, they're brittle. Old rule of thumb when I was an apprentice was if you dropped a tap on the concrete floor, pitch it as it would likely break next time you used it.
As for removal, as Rusty commented use compressed air, vacuum, small picks, whatever you can find to fish most of the chips out. Then see if needle nose will turn or wiggle it. If the thing is loose enough to move then half your battle is won.
If not it's been my experience that there are three ways to remove a tap.
1) Brute force involving hammers and punches to break it out and pick out the pieces. Works better with through holes and in steel.
2) Acid, used to be a kit you could by called "Tap Out", came with putty to make a damn to contain the acid though with aluminum and stainless it wasn't much necessary. Basically dissolves the tap, works great in aluminum and stainless which are not affected by the acid but not carbon steel. Takes sometimes several cleanings and repeat applications because as the acid works it becomes depleted in effectiveness.
3) Plunge EDM, often called a Tap Burner. Call around to machine shops to see if they have one, pretty specialized piece of equipment so not all shops will have one. Uses a tubular electrode through which coolant is run while the machine uses electric current and packs at the tap core disintegrating it and flushing out the bits. Works really well but may cost a few bucks depending on what they want for shop time, shouldn't take more than an hour set up and everything.
Best of luck how ever you choose to go. The floor of the cam cavity in the head can be repaired by a decent welder but it may be easier and cheaper to replace it and have it repaired later as a back up.