I know bitcoin core is the most popular/suggested software to run a full node, but are there other options? I've heard of others like Bitcoin Unlimited. My question is, would those nodes running alternative software still have to have that software adhere to the protocol rules of bitcoin in order to be a full node on the network?
No anyone can design their own.Its just that rules and coding knowledge is required.Armory wallet is the best alternative to bitcoin i can recall myccpay