How can/should I repair this roof damage caused by a fallen tree limb?
All the shingles you have pictured need to be replaced. It is a matter of easing up the shingles far enough to gain access to the nails, pull them out without ripping the shingle(s) up, it will also require easing up the shingles above the damaged ones and pull THOSE nail out of the way too since they are going through the top of the next course down. Eventually the shingle will practically fall out and you can replace the shingle in reverse order.

If you are fortunate, the roof has not gotten hot enough to bond the shingles together. On 3 tab shingles the asphalt dabs that come with the shingle to bond the tabs of one row to another are easy to separate. The architectural shingles I replaced my 3 tab shingles with, the asphalt dabs were a different story. The three tab shingles popped up best while the roof was cool, while the architectural shingles needed a heat gun set to get the shingles really hot, but not so hot to melt them (the shingles), but enough to get the bond to release. I hope you do not have to go that route.

I use a ripping bar to ease the shingles up, I have not had any luck with any other style bar, unless I sharpened the edge a bit.