1. He called on his uncle.

2. He called at his uncle's (house).

3. He visited his uncle.
4. He visited his uncle's (house).

5. He dropped by the bakery/his grandma.
6. He came by the bakery/his grandma.

7. He paid a visit to his uncle.
8. He paid a visit to the bakery.
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Are they all grammatical? Are there any errors in usage? Do you have some more verbs which have similar meanings?

All are grammatically correct, but 4 and part of 5 and 6 don't make good sense.

4. I understand visiting his uncle, but why would he visit the house?

5. I understand dropping by the bakery, but not dropping by his grandma.

6. I understand coming by the bakery, but not coming by his grandma.

How can you fix those three things?

4. He visited his uncle.

5. He dropped by the bakery.
6. He came by the bakery.

Yes.

3 and 4 are the same.

5 and 6 are now fine.

Yes, all of the sentences you provided are grammatically correct and do not contain any errors in usage.

Here are some additional verbs that can be used to express similar actions:

1. He phoned his uncle.
2. He rang his uncle.
3. He texted his uncle.
4. He emailed his uncle.
5. He messaged his uncle.
6. He wrote to his uncle.
7. He sent a letter to his uncle.

All of these verbs can be used to convey the action of communicating or reaching out to someone.