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Create static block and using single category id which product display and given number as you wish here example after create static block magento :-
{{block = "catalog/product_list" category_id="3", num_product="" limit="certain number here" template="template path here"}}
Hope this help
Create a static block with number of product you want to show. then identify that the user is login with is_login() function.so function will be like Is_login() {//Static block code
}hope that work!!!