Shopify Subscription - Select Multiple products for each subscription order

[Nidheesh]

Looking to build an app which is capable of allowing the customer to choose multiple products within a Subscription plan and also the products can be different for each subscription order. While looking into the Shopify Subscription API, it looks like the subscription to be assigned to each product.

1. Is it possible to create a subscription plan in such a way that the customer can choose the product he wants?
2. Can the price adjusted to provide a discounted price for each product in the subscription?
3. Is it app's responsibility initiate the subscription order?
4. Is it possible to change the products / the final amount of each subscription order?