changing the cursor is easy with its css properties :

http://www.w3schools.com/css/pr_class_cursor.asp

changing the look and feel of the select is done by styling both the SELECT and OPTION tags. the styling is very limited and may look different on various browser. thats why the best practice in web design is not to use the select. instead we use lists and award them with behavior using javascript.

you can check heep.co.il search drop down to fully understand the technique. 

also, here a few methods that should work as well:

http://www.tyssendesign.com.au/articles/css/dropdown-low-down/