Add required test suite and websocket fixes

tests/test_pool.py

@@ -1,2 +1,37 @@
-def test_placeholder_pool():
-    assert True
+import pytest
+
+from app.pool import PoolValidationError, get_question, parse_pool_json, public_question_payload, question_time_limit
+
+
+def test_pool_validation_accepts_well_formed_pool(sample_pool):
+    pool = parse_pool_json(sample_pool)
+    assert pool["title"] == "Sample Quiz"
+    assert pool["score_fn"] == "linear_decay"
+    assert question_time_limit(pool, 0) == 2
+    assert get_question(pool, 0)["correct"] == "B"
+    public = public_question_payload(pool, 0)
+    assert "correct" not in public
+    assert public["options"]["A"] == "Alpha"
+
+
+@pytest.mark.parametrize(
+    "mutator, message",
+    [
+        (lambda p: p.pop("title"), "title"),
+        (lambda p: p.update({"questions": []}), "at least one"),
+        (lambda p: p["questions"][0].pop("text"), "text"),
+        (lambda p: p["questions"][0].update({"options": {"A": "x"}}), "options"),
+        (lambda p: p["questions"][0].update({"correct": "E"}), "correct"),
+        (lambda p: p.update({"score_fn": "missing"}), "Unknown"),
+        (lambda p: p.update({"time_limit_default": 0}), "positive"),
+    ],
+)
+def test_pool_validation_rejects_invalid_shapes(sample_pool, mutator, message):
+    mutator(sample_pool)
+    with pytest.raises(PoolValidationError, match=message):
+        parse_pool_json(sample_pool)
+
+
+def test_pool_validation_rejects_invalid_json():
+    with pytest.raises(PoolValidationError, match="Invalid JSON"):
+        parse_pool_json("{bad")