If the wife, who has filed the case under Section 498-A IPC against her husband, is herself willing to stand surety for the bail of the accused husband, then why not settle the case?
Offence under Section 498-A IPC is a non-compoundable offence. However, there are ways of compromising / settling / compounding certain non-compoundable cases too. I have explained it in one of my YouTube videos:
In your case, if the case is still under investigation, then the police may perhaps file a closure report on the request of the complainant wife on the ground of having settled the case. But, if the case is charge-sheeted, then both the parties can approach the high court for quashing of the case on the ground of mutual consent having compromised the case and now living together peacefully.
Once there is a non-bailable warrant issued for execution by police, the police can arrest the accused and produce him before the court which issued the NBW. Thereafter, it is up to the court to send him to custody or grant him bail for appearance on next date. Yes, the police can execute this NBW immediately.
An application for recall / cancellation of the NBW can be filed before the court which issued it. The accused may be asked to remain present for this application. If the court is convinced, it can cancel the warrant. The application is of miscellaneous nature and the format can be seen from your local court. Generally, it is a simple type of format.