I don't think they even offer Miva anymore, but probably still have Miva sites hosted from when they did -- but ZenCart is in the one-click installation section and you can always install the cart of your choice on your own.
Any $97 code will give you $97 on yearly plan -- if that's how the user set them up. They can assign a different rate to each plan. I just put the max on all of them, which ranges from $50 on the cheapest monthly plan, up to $97 on all 1 & 2 year plans. So, even on the cheapest monthly plan, it's still like getting free setup.
No, but depending on the cart you use, I'd imagine you would mostly be using their "add products" section, or adjusting the look & feel with code mods or templates/themes. There are free editors out there like Nvu, or commercial ones like Dreamweaver, where you can create the sites on your computer then upload them via FTP. But most shopping carts are their own websites that you just add products & categories to.
If it's not part of the cart's functionality, you can always add mods, change code, etc. Doesn't sound like that would be a problem.
Edited to add: I forgot to mention that I tried Miva here years ago and didn't like it. And at that time, DH had some problems with it and couldn't get help from Miva, which led to a lot of Miva users having days of downtime.
Carts like Zen, osCommerce, etc... have a huge following and if you can't get help here, there's probably nothing you would ever need to know that a quick Google search couldn't bring up.
Save up to $96 at Dreamhost with ALMOST97 promo code (I get $1).
Or save $97 with THEFULL97.