1. I am not sure what algorithm you are exactly talking about but it is possible to solve the mentioned problem using offline techniques (I cannot think of an easy offline algorithm that has O(n*log(n)) complexity), but the main usage of the DS is when using it online. Most of the problems I mentioned need the algorithm to be online and since writing the post I encountered a lot of problems which are solvable using the DS and all need the DS to be online(One big application of the DS is doing undo priority queue in O(log(n)) on dsu).
2. You are correct to note that what I described has simmilarities with krusakl reconstruction tree, espically the warmup problem (which krusakl reconstruction tree can solve), but the rest of what I dsecribed cannot be done with krusakl reconstrucion tree since it doesnt support edge insertions. I highly advise you to read the post again in order to understand what my DS supports.

Undoing operations online is quite hard. This is a solution to the online problem without undoing operations: Maintaing mst with onl8ne edge insertions You can use offline deletion trick on the above DS for your general problem. Hope it is still relevent