DFS that is quadratic for no reason

This connected-components counter is textbook DFS, and it returns correct answers. Yet on a graph with 2 · 10^5 vertices and 2 · 10^5 edges it takes 40 seconds and uses gigabytes of memory, while the same algorithm in Python finishes in under a second. Nothing is wrong with the algorithm. Find the bug.

1#include <iostream>
2#include <vector>
3using namespace std;
4 
5void dfs(int u, vector<vector<int>> adj, vector<bool> visited) {
6  visited[u] = true;
7  for (int v : adj[u])
8    if (!visited[v]) dfs(v, adj, visited);
9}
10 
11int countComponents(int n, vector<vector<int>> adj) {
12  vector<bool> visited(n, false);
13  int components = 0;
14  for (int u = 0; u < n; ++u) {
15    if (!visited[u]) {
16      ++components;
17      dfs(u, adj, visited);
18    }
19  }
20  return components;
21}
22 
23int main() {
24  int n = 5;
25  vector<vector<int>> adj(n);
26  auto add = [&](int a, int b) { adj[a].push_back(b); adj[b].push_back(a); };
27  add(0, 1); add(1, 2); add(3, 4);
28  for (auto row : adj) { for (int v : row) cout << v << ' '; cout << '\n'; }
29  cout << countComponents(n, adj) << "\n";   // prints 5, expected 2
30}

1. The output is 5, not 2. Explain why every vertex is counted as its own component even though the DFS runs.
2. Estimate how much data is copied per dfs call, and the total work for V = E = 2 · 10^5.
3. Fix the signatures. Which parameters should be const&, which &, and why?
4. There is a third, subtler copy in main. Find it.
5. State the complexity before and after.