[SalesForce] Validation rule to prevent field update

As per your validation rule, every time record is edited or updated, rule is satisfying.

If I understand your requirement correctly, you want to fire validation rule during creation and if the status is not New. If that is correct the updated rule will be like this:

ISNEW() && NOT(ISPICKVAL( Status__c, 'New'))

The problem is that the Asset won't be linked to the opportunity when you use the Create a Record action, so you'll need one of four alternatives.

First, you could create a lookup on the Asset to link it to the Opportunity. Then, you'd have a second Process on the Asset to complete linking the records. If this sounds unnecessarily complicated, you're right, but it's the only way to do this that I'm aware of without putting additional moving parts in play.

Second, you could create a Flow that is called instead of the Create a Record action. From there, you will have the ability to set variables so that you know what Asset you just created, allowing you to complete the process of linking the records together.

Third, you could just create an Invocable Method. This means you'll have to write and deploy Apex Code, but at least it would be relatively painless compared to trying to build this in the UI. However, if you've already gotten as far as considering this option, then...

Fourth, you could just write a trigger. Process Builder isn't well-suited for things like multi-level record creation. It's a simple tool that allows you to create trivial inserts and updates, but this kind of use case is where the limitations become pretty obvious.