diff --git a/lib/aggregate.js b/lib/aggregate.js
index 7faea5eeb66..a506cf20cf0 100644
--- a/lib/aggregate.js
+++ b/lib/aggregate.js
@@ -13,7 +13,7 @@ const readConcern = Query.prototype.readConcern;
 
 /**
  * Aggregate constructor used for building aggregation pipelines. Do not
- * instantiate this class directly, use [Model.aggregate()](/docs/api.html#aggregate_aggregate) instead.
+ * instantiate this class directly, use [Model.aggregate()](/docs/api.html#model_Model.aggregate) instead.
  *
  * ####Example:
  *
diff --git a/lib/helpers/query/castUpdate.js b/lib/helpers/query/castUpdate.js
index d0fe88955c6..7cd9c5aa5ad 100644
--- a/lib/helpers/query/castUpdate.js
+++ b/lib/helpers/query/castUpdate.js
@@ -411,7 +411,7 @@ function castUpdateVal(schema, val, op, $conditional, context, path) {
     return schema.castForQueryWrapper({
       val: val,
       context: context,
-      $skipQueryCastForUpdate: val != null && schema.$isMongooseArray
+      $skipQueryCastForUpdate: val != null && schema.$isMongooseArray && schema.$parentSchema
     });
   }
 
diff --git a/lib/schema.js b/lib/schema.js
index f6550e3a28d..8afef3ca9e1 100644
--- a/lib/schema.js
+++ b/lib/schema.js
@@ -853,8 +853,12 @@ Schema.prototype.hasMixedParent = function(path) {
  * @api private
  */
 Schema.prototype.setupTimestamp = function(timestamps) {
-  const childHasTimestamp = this.childSchemas.
-    find(s => s.schema.options.timestamps != null);
+  const childHasTimestamp = this.childSchemas.find(withTimestamp);
+
+  function withTimestamp(s) {
+    const ts = s.schema.options.timestamps;
+    return ts == true || ts == null;
+  }
 
   if (!timestamps && !childHasTimestamp) {
     return;
diff --git a/test/model.update.test.js b/test/model.update.test.js
index 9ce93be7409..d18efa7d9dd 100644
--- a/test/model.update.test.js
+++ b/test/model.update.test.js
@@ -2536,6 +2536,48 @@ describe('model: update:', function() {
         catch(done);
     });
 
+    it('doesn\'t skip casting the query on nested arrays (gh-7098)', function() {
+      const nestedSchema = new Schema({
+        xyz: [[Number]]
+      });
+      const schema = new Schema({
+        xyz: [[{ type: Number }]],
+        nested: nestedSchema
+      });
+
+      const Model = db.model('gh-7098', schema);
+
+      const test = new Model({
+        xyz: [
+          [0, 1],
+          [2, 3],
+          [4, 5]
+        ],
+        nested: {
+          xyz: [
+            [0, 1],
+            [2, 3],
+            [4, 5]
+          ],
+        }
+      });
+
+      const cond = { _id: test._id };
+      const update = { $set: { 'xyz.1.0': '200', 'nested.xyz.1.0': '200' } };
+      const opts = { new: true };
+
+      return co(function*() {
+        let inserted = yield test.save();
+        inserted = inserted.toObject();
+        assert.deepStrictEqual(inserted.xyz, [[0, 1], [2, 3], [4, 5]]);
+        assert.deepStrictEqual(inserted.nested.xyz, [[0, 1], [2, 3], [4, 5]]);
+        let updated = yield Model.findOneAndUpdate(cond, update, opts);
+        updated = updated.toObject();
+        assert.deepStrictEqual(updated.xyz, [[0, 1], [200, 3], [4, 5]]);
+        assert.deepStrictEqual(updated.nested.xyz, [[0, 1], [200, 3], [4, 5]]);
+      });
+    });
+
     it('defaults with overwrite and no update validators (gh-5384)', function(done) {
       const testSchema = new mongoose.Schema({
         name: String,
diff --git a/test/timestamps.test.js b/test/timestamps.test.js
index fe0564e3ef8..8c574dbd0ba 100644
--- a/test/timestamps.test.js
+++ b/test/timestamps.test.js
@@ -4,6 +4,7 @@ const assert = require('assert');
 const start = require('./common');
 
 const mongoose = start.mongoose;
+const Schema = mongoose.Schema;
 
 describe('timestamps', function() {
   let db;
@@ -162,4 +163,21 @@ describe('timestamps', function() {
       });
     });
   });
+
+  it('no timestamps added when parent/child timestamps explicitly false (gh-7202)', function(done) {
+    const subSchema = new Schema({}, { timestamps: false });
+    const schema = new Schema({ sub: subSchema }, { timestamps: false });
+
+    const Test = db.model('gh7202', schema);
+    const test = new Test({ sub: {} });
+
+    test.save((err, saved) => {
+      assert.ifError(err);
+      assert.strictEqual(saved.createdAt, undefined);
+      assert.strictEqual(saved.updatedAt, undefined);
+      assert.strictEqual(saved.sub.createdAt, undefined);
+      assert.strictEqual(saved.sub.updatedAt, undefined);
+      done();
+    });
+  });
 });