It's imposible for me to answer this question for you. It depends on far to many unknown factors.
How comfortable you are using eCart
How Knowledgeable you are with the development concepts and practices needed for each of the requirements you list.
How fast you work.
a good developer could have this completed in as little as a couple of days, but I really cant say how long it will take for you to complete it.
eCart can create the add to cart system, and the checkout system
the checkout can be cancelled at any time.
you will need to add the delivery or pickup choice, and the delivery or pickup time choice to the checkout page.
you can configure rules in eCart to charge shipping and show those charges, how long it will take to configure this in eCart depends on how complex it needs to be
the eCart display manager can be used to add a quick cart to each page that shows a running total and quantity count,
for creating the account, you will need to use security assist, sending the email, you will need to use Universal Email. There are tutorials on the eCart support page for adding registration to your cart.