yes wife can sue her husband
An ex-wife cannot sue her ex-husband for money earned by his current wife unless there is some type of contract between the three of them.
No. If your present husband is the father of the children of his previous marriage and is the custodial parent he would have to sue his ex-wife (the children's mother) for support.
You can successfully sue if you can show damages such as to your property.
If the wife doesn't want him to and he does it anyway, she can probably sue him.
yes
No. There is no privacy when you are married.
Short answer- no.
Yes of course if he has custody.
Unless you have committed an criminal offense, she can't sue you for any reason.
The husband may be able to press stalking charges, if he has asked her to stay away.
In the US, anyone can sue anyone for anything. The question is not whether you can sue, but whether you can win. Lying about marital status is not an actionable claim, and the mistress would not win.