Does it make a difference to validity whether there is.
1. Almost no sex (let's assume on his birthday once per year she gifts him sex as a "present").
If the wife doesn't intend to have children, then there would be no marriage. Even if she intends to have children, in this case she is sinning againt her vow, repeatedly, monthly, yearly, every single time the husband reasonably requests relations.
How one judges the intent to have children? I have no idea. The Church probably rules this is a valid marriage but the wife is a habitual/continual vow-violator.
2. No sex after the honeymoon. If other words some at the very beginning and then none, like for example she tried sex didn't like it and was completely turned off the idea (I know of this exact example and they are both Trads living in Spain).
There is still the obligation to have children, which if not attempted violates the vow. Does this nullify the marriage? I have no idea, but I would think that it could be annulled if it is proven that the wife is done "trying", especially after only a short time in the attempt. As above, even if it is valid, she is a repeated/continual vow-violator and is in grave sin.
3. Either of the above but in those 10 years she had 1 child and that is now "enough".
What ASPECT invalidates the marriage? If it is just intention then it is present in all of the above examples.
Valid marriage but the wife lives in a constant state of sin for her lack of providing the marriage debt and (probable) intention to avoid children (without husband's agreement).