You can remove the coupon code from the cart page without any effect on the functionality. You can alter the top header image from within the main.dwt template file, in here you can alter any of the common design elements that you see across the front end pages. It uses standard css for the formatting so you can use whatever image you would like and you will be able to make any adjustments to the css that you need to.
If you have a bookmark this page script you can put it into the main template, or you can just add it in to any of the pages content areas. There is no feature of the store that allows you to add this option automatically.
There is no send as gift functionality built into PowerStore, it might be possible to add this in but that would be a custom endeavor.
It is technically possible to add in other shipping options or to calculate the shipping before you get to the confirm page but how to go about it all depends on exactly what you would like to do. If you want to add in your own shipping rules you can set it up to display those charges on the cart page. If you are using the shipping quotes from UPS or FedEx you will not be able to see the shipping charges until you get to the confirm page.