Must a customer create an account, or can this be done automatically during checkout?

I'm afraid I may scare away potential customer's by "forcing" them to create an account. Ideally, I'd prefer if their account was automatically created during the checkout process. The customer could make their purchase, and their account would be created when they provided the details of their shipping address, email address, etc. during checkout.

Is there a way to either turn off the "create account" option or at least make it less obvious that a customer is creating an account when purchasing an item?

There are several "Checkout" mods in the PLugins Section. Just browse for one you like and see what the dedicated threads have to say about them.

Also, you can customize all text in the "create account" page to downplay the fact that they are creating an account - really, you should only be requesting information from them that you will need to process and ship their purchase, and Zen Cart internally calls this information an "account", which it must retain for accounting purposes. The password for the customer to access their information later is the main account-like feature which can't be eliminated without one of the COWOA-type mods.

I've been perusing the Plugins section as per dbltoe's suggestion

So far I've found one COWOA mod that works with v.1.5.1, which is what I'm using.

See: http://www.zen-cart.com/downloads.php?do=file&id=1416

I've also found a Fast and Easy Checkout for Zen Cart for v.1.5.0 at http://www.zen-cart.com/downloads.php?do=file&id=594