Generally, American and Canadian citizens may cross the border without visas or passports. However, it is always a good idea to carry identification with you, especially if you are a naturalized citizen. Citizens of other countries should have a passport or appropriate papers. Both countries accept a valid driver's license of the other country. Proof of insurance is required if there is an accident.
Laws vary from province to province and state to state.
Make sure you have you vehicle registration with you. Use of seatbelts is mandatory in Manitoba. Cats and dogs are welcome in both countries provided they are in good health and have a current rabies vaccination certificate, if they are over three months old. Other animals are subject to restriction. Yes, and you will get the best rate at a currency exchange or bank close to the border.