No, aller doesn’t necessarily mandate a y, especially in the first sentence you cite where the destination is not suggested but where I might not use aller either in a French translation.

On the other hand, while it is correct to state we can say ça va ?, ça y va ? is also possible with a different meaning.

No you shouldn’t use y whenever you use the verb “aller”.
The two main reason to use y are :

You already know the destination and you don’t want to repeat it :

• Tu vas à l’école ce matin ?
• Oui j’y vais.

The second option is when you don’t know the destination or there is no interest in telling :

• Je vous laisse, je dois y aller.

The main idea is that y replace the destination when you don’t precise it.

So for your question about “ça va ?” is that the verb “aller” is not meant as moving but as the current state of someone or something.

• Tu vas bien ?
• Oui ça va.

In this case there is absolutely no destination, so you can’t add y.

As already said “ça y va” would mostly be use as equivalent of “it goes there”, but as you probably already know, french people prefer using “il” or “elle” instead of “ça” for the translation of “it”.

“that goes there ?” would be translated to “ça va là ?”.

“ça y va ?” would be used when “ça” already appeared before.

• A quoi ça sert ?
• Ca sert à mettre le linge au sous sol
• Vraiment ? Ca y va ?

It is really hard to find a good example for this one because it is not that common.