Loose equality in a deduplicator

A data-cleaning step removes duplicates from a stream of parsed values and then finds the index of a target. Users report that 0, "", false and null collapse into one value, that NaN is never found even when present, and that indexOf(NaN) returns -1. Find every equality bug.

1function dedupe(values) {
2  const out = [];
3  for (const v of values) {
4    let found = false;
5    for (const u of out) {
6      if (u == v) { found = true; break; }
7    }
8    if (!found) out.push(v);
9  }
10  return out;
11}
12 
13function findIndex(values, target) {
14  for (let i = 0; i < values.length; i++) {
15    if (values[i] === target) return i;
16  }
17  return -1;
18}
19 
20console.log(dedupe([0, '', false, null, undefined, '0', NaN, NaN]));
21// [0, null, '0', NaN, NaN]  — expected [0, '', false, null, undefined, '0', NaN]
22console.log(findIndex([1, NaN, 3], NaN));        // -1, expected 1
23console.log([1, NaN, 3].indexOf(NaN));           // -1
24console.log([1, NaN, 3].includes(NaN));          // true

1. List which pairs among 0, "", false, null, undefined, "0" are == equal, and explain the coercion rules that make them so.
2. Why is NaN === NaN false? Which built-ins use which equality algorithm?
3. Rewrite dedupe in O(n) using the right equality semantics, and fix findIndex.
4. When is == acceptable in modern code?
5. State the complexity before and after.