Does the order of columns has a significant effect on INSERT? Do we experience a noticeable difference in performance for these two queries?

INSERT INTO table (col1, col2, col3, col4, col5) ...


and

INSERT INTO table (col5, col3, col1, col2, col4) ...


Do we need to arrange INSERT columns according to the order of columns in the table?
No, you don't need to gave the columns in the same order. Not least, table order may not reflect actual on-disk order (this is 100% true for SQL Server, and I'm sure MySQL is the same)

Unless your OCD itch needs scratched