how to do this custom coding?

zencart provide $options_menu to list products properties such as colors , sizes. but this var is containing html code.
My html deisin must chage the html struture, for this reason I must get the arrray bellow, how to do it ?

how to set diffrent prices for the same product with diffrent styles?

You could always just set it up so there's the four product options you talked about under one dropdown box, ie instead of having a box for color and a box for size you could have one which has:
blue medium
red medium
blue small
red small

That would mean the user only has to click on one dropdown box as well, which is surely a good thing since there aren't so many choices anyway?

how to add shopping cart info on head of site?

This, maybe:

http://www.zen-cart.com/downloads.php?do=file&id=990

the default template list new products by random. the products changes when refresh the page.
now I want to list the latest product by date. how to do it ?

how to add a diy page which can use zencart functions and constants?

the page can use zencart functions and constants.but it must not include any template php files ,such as tpl_header.php.
I want to use this page to do ajax request feedback.

for example:
this page i named it as ajax.php ,
i want to add ajax in product_info page, in js code ,i use jquery,

$.ajax({
url:"http://localhost/includes/templates/my_template/ajax/ajax.php",
...
success: function(html){
$("#hello").html(html)
}
});

if the ajax.php contains head or foot html code, these code are not my needed code,the ajax return code is not clean.

how to add this type of diy page?

only know the product id , such as 10
how to get product name ,image, category id from products_id?
need sql or any zencart function?

$product_name = zen_get_products_name($product_id[,$language_id=$current_language_id]);
$category_id = zen_get_products_category_id($product_id);
$image = zen_get_products_image($product_id[,$width=SMALL_IMAGE_WIDTH,$height=SMALL_IMAGE_HEIGHT]);

... where the parameters in [brackets] are optional and the default values are shown. All functions are in /includes/functions/functions_lookups.php.

thank you very much