For the UPDATE
Use:
UPDATE table1
SET col1 = othertable.col2,
col2 = othertable.col3
FROM othertable
WHERE othertable.col1 = 123;
For the INSERT
Use:
INSERT INTO table1 (col1, col2)
SELECT col1, col2
FROM othertable
You don’t need the VALUES syntax if you are using a SELECT to populate the INSERT values.