Does a divorce issued with the intention of threat and anger take effect, knowing that it is the second divorce, and is it permissible to marry her after the 'iddah period ends with a new contract and dowry to annul the two divorces, and what is forbidden for her during the 'iddah?

If you utter the divorce while being aware of what you are saying, then the divorce has occurred.

If you take your wife back during her iddah (waiting period) or marry her after its expiry with a new contract, she returns to you, and the remaining divorces (out of the three allowed) will apply, if she has not married anyone else. This is also the case even if she married someone else and then returned to you, according to the majority of scholars.

A revocably divorced woman (during her iddah) is considered in the status of a wife. Her husband is permitted to do with her what is permissible with his wife, and she may adorn herself for him. However, she is not allowed to leave the house except out of necessity. Scholars have differed on her leaving during the day to attend to her needs. The Hanafis and Shafi'is are of the opinion that she is not allowed to leave neither at night nor during the day, while the Malikis and Hanbalis permit her to leave during the day for her needs, but she must stay in her home at night.