What is the legal requirment to use "TM" or "®"?

The TM symbol indicates a claim of trademark rights. The marking may indicate that a trademark application is pending or may indicate a common law mark (rights based on actual use and not necessarily pending with the IP office).

The SM symbol indicates a claim of service mark rights (i.e. a pending or common law mark for web services rather than a product).

The ® indicates registered trademark rights, meaning that you have filed a trademark application with the relevant country IP office and subsequently have been granted a registration from that IP office.

Hope this helps.