1) Instead of using PayPal Payments Standard, you should sign up to use Paypal Express Checkout:
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using Express Checkout is free.
you can then delete the checkout form on the checkout page.
2) yes, the cart will carry over all of the shipping charges to paypal.
3) Inventory control tracks the number of items you have in your store against the items being purchased to ensure that you will be able to fulfill the order.