I attached a picture of the tiles along putter edge of roof. I'm sure these need to be repaired and why I have water coming into plaster walls.. Cansomeone please help me identify these and possibly tell me where I can purchase replacements. Thanks in advance!

Was trying to replace some ~12 year old architectural timberline shingles in Florida recently. I think it was like 110 with heat index. I would probably get 1st degree burns even through my pants if I was kneeling/sitting on the shingles long enough, kind of like walking in the street barefooted on a hot day. Basically the architectural shingles are a 3 tab shingle with half of a second layer on top of that (called the saw tooth shingles). Some of the saw tooths were lost in the hurricane but the main 3 tab shingles are fine. I wanted to replace some of these though. I read it's not recommended to do shingles above like 85° but then how do people do roofs in places where it's hot most of the time? I could not even tap a putty knife under the shingles lightly using a hammer is what I'm saying. The shingles are soft in the heat but the tar strips under the shingles are so solid felt like I was hitting a nail on a few of them but I would move the putty knife over a bit and got the same thing, I could not get the putty knife under - It would be very tedious and take like 45 minutes just to release one shingle (have to remove the two shingles above it to replace and some are also tied into ridge shingles). Have to be very careful or the putty knife can go right through the shingle and ruin it. I just left it how it is for now because the main 3 tab shingles are all fine and an insurance claim is being made. My question though is how do you replace just one shingle when it's this hot? Is there a trick like to cool them down with ice water lol? I worked for a roofer briefly in Winter in like 30 degrees NY and they had a guy who just sat there all day with a blow torch thing heating up shingles one by one out of the bundles. The roof (tar) was soft from the heat so I would think a putty knife would go easily between the shingles but it was damn near impossible. anyone experienced with this? I'm not trying to fix it now, I just want to know the trick if there is one. Thanks.