1.) The only way to remove the "Add to Cart" button is to go into Exchange > Add-ons and disable the Multi-Item Cart add-on. You can use CSS to hide the button, but if you're not using the Shopping Cart, instead of hiding the button, it'd be best to disable the Multi-Item Cart add-on.
2.) There isn't an option to change this in Exchange at this time.
3.) Even new users should be able to see the coupon option when making their purchase. They (like previous customers) won't see it until they've finished the registration form and are actually making the purchase. Make sure you have the Basic Coupon add-on enabled (Exchange > Add-ons). Also make sure that you're running the latest version of Exchange and all add-ons. If neither of those options work, try testing for a plugin conflict by deactivating all of your plugins except for Exchange and then see if the coupon option shows during registration/purchase. If it does, reactivate all your other plugins one at a time, checking Exchange each time to see which plugin is creating the conflict.
Also, I don't know if it's the same site, but when looking at your site for your other post (http://ithemes.com/forum/topic/52208-shipping-price-error/), I was able to enter a coupon as a new, first-time registered user.
4.) There aren't any settings to do this in Exchange. You can do this by creating and editing template files, but I do not recommend you do this unless you are comfortable with what you are doing in that aspect.
5.) There isn't a way to change "Login" to "Create New Account" for just new customers. If you change it to "Create New Account," that's how it will show for all users, new or previous. The easier way to accomplish this would be to use both the Login link and the Registration link.
6.) If you make changes directly to any of the stylesheets in Exchange, any time you update Exchange, your changes will be overwritten. What you'll want to do is create an "exchange" folder in your theme (ex: wp-content/themes/YourTheme/) and, in that folder, you'd add a style.css file that you created with the CSS you want to use.
You can make any feature requests you have here: http://ithemes.com/exchange/feature-request/