Thanks for your interest in Exchange and the Exchange add-ons.
With Exchange and the Membership add-on, you can create membership products and restrict content to that particular membership. While there is a Multi-item Cart add-on, you do not have to enable it in Exchange. And there is a Store page, but you can either disable it, or just rename it (both the page title and page slug) in your Exchange settings to something that would better suit your particular situation.
Using the Recurring Payments add-on,
We're working on a demo site for memberships here: http://demos.ithemes.com/ithemes-exchange-membership/ You can actually "purchase" one of the demo products and checkout what the account page would look like. You can use the Stripe option with one of the test card numbers listed here: https://stripe.com/docs/testing
I'm not sure I understand the question. The MailChimp add-on for Exchange just adds users to your lists in MailChimp. You still have to go into MailChimp to create and send your emails. If the customers are already on the list, even if they don't check to register for your email, they're already on the list and not checking to opt-in won't remove them from the list. If I misunderstood the question, just let me know and I'll do my best to answer.
You can set up recurring payments so that they are automatically recurring or not automatically recurring. If it is not automatically recurring, at the end of the month/year, the membership ends until they repurchase the product. If it is an automatically recurring payment, the customer will be charged every month/year until they cancel their subscription. If a payment is declined for some reason, it ends their subscription and they will have to repurchase the membership.
Yes, you can disable the cart. There isn't a wishlist option in Exchange at this time and you'd have to be more specific on the other "icons & tools" for me to say for sure on those.
There is an account page you can customize for your customers, but there isn't an option to make a custom account page based on the customer or their subscription dates.
Do you mean on the customer's profile page? If so, they can update their information there, but it doesn't actually display. Of course, if you have programmers who are capable, you are welcome to customize Exchange however you'd like in order to suite your needs.
Let us know if you have any additional questions!