Ok, first what you need to do is represent the tree as array (using in-order). For every vertex you will have from[v] and to[v] (the range in the array that is the subtree of v) .Then put all the vertices and the queries in the same array and sort them in non-increasing way. When you are at a vertex you must make seg[from[v]]+=1 and seg[to[v]+1]-=1 . Now when you are facing a query you must simply output the sum [1,from[v]]

First make a list of queries for every node, then do a DFS keeping an order-statistic tree, like a treap or the policy-based data structures from the STL. When you enter a node, you add the value to the tree, when you exit the node you remove the value. To answer a query, just find the order of the first key greater than c in the tree.

You can do one dfs keeping all ancestors of current node in an order statistics tree keyed by node weight. Answering queries for current node is just counting number of elements in the order statistics tree with value > c