Are there any functions in MySQL like dense_rank() and row_number() like Oracle?

Mysql doesn’t have them, but you can simulate row_number() with the following expression that uses a user defined variable:

(@row := ifnull(@row, 0) + 1)

like this:

select *, (@row := ifnull(@row, 0) + 1) row_number
from mytable
order by id

but if you’re reusing the session, @row will still be set, so you’ll need to reset it like this instead:

set @row := 0;
select *, (@row := @row + 1) row_number
from mytable
order by 1;

dense_rank() is possible but a train wreck; I advise handling that requirement in the app layer.