I have been using and setting up several versions of Abantecart since Oct 2013. I have several sites that are in subdomains and they work fine.
As to rather you need to install the cart in each subdomain, depends on rather they all have the same products database or different ones. Abantecart has a good multistore function where sub-store is required to be in a subdomain or different domain, but it does not have separate complete installations for each subdomain. All stores have access to the same database, but each store can show their own products and pricing and have their own template setup. This works best as in the case of a retailer with multiple locations.
You can read about it here
http://docs.abantecart.com/pages/settings/stores.htmlIf each of your sites is a different type of store with different inventory, say one is a t-shirt store and another sells electronics then I would suggest you treat each as an independent installation. tvstore.mymaindomain.com and tshirst.mymaindomain.com, etc.
I am providing sites for franchise distributors who all have access to the same inventory, but are all unique independent businesses. Initially I had hoped the multistore would work, but since each of my distributors is a stand alone business I decided it was best to treat each one as a totally unique installation on their own domain name, and use a master inventory store that I use to update each store's product list. If these had all been company stores, with store managers I would have used multistore setup.
I hope this helps you understand better. Since Abantecart is open source, best way is to try a setup and see how it plays out for you in what you want to accomplish.
Just another abantecart user, but a happy one!
Lee