G: use ETT + Segment Tree (Fenwick Tree usable also). Make sure to use LCA with time complexity $$$O(\log n)$$$ or lower.

this blog may help https://codeforces.me/blog/entry/78564

https://cp-algorithms.com/graph/tree_painting.html

You can also refer this blog, small modifications in given code will also work.

How to solve problem D. I am confused about the statements.

It is bad, that this problem is quite implementation heavy and is very common, and I had the solution for almost this problem on one archive.

There are two ways to do it.

$$$A$$$. Let's precompute sum on pathes from $$$v$$$ to $$$root$$$. Then answer for $$$v$$$ and $$$u$$$ is $$$sum[v] + sum[u] - 2 \cdot sum[lca(v, u)]$$$, where $$$lca(v, u)$$$ is the least common ansestor of $$$v$$$ and $$$u$$$, which can be calculated using binary lifting. How to answer queries? Well, the query here means "add $$$x$$$ to $$$sum$$$ of all vertices in subtree of vertice $$$v$$$". How we can add value on subtree quickly? There is a technique, which uses some properties of $$$dfs$$$. Let's simply run dfs and every time we visit a vertice or return to it from child, append it to some global array $$$dfsarr$$$. Look at some vertice $$$v$$$: it appears in array several times, and the segment from $$$leftmost[v]$$$ to $$$rightmost[v]$$$ contains all vertices in subtree of this vertice (just draw it, and you will see). Now, instead of working with original array of numbers on vertices, we use that $$$dfsarr$$$. All remaining is range sum: we can use fenwick tree of segment tree.

$$$B$$$. Way for not smart but strong coders. You can use heavy-light decomposition. It is not easy structure and a bit overkill, but I submitted this, because I already had it prewritten.