Lets assume a team has a stock brokerage company registered in Jurisdiction outside of USA, e.g. Singapore or Australia.
1. If this stock brokerage want to add cryto exchange to their business, and offer crytocurrency trading account opening and deposit of crytocurrencies to USA Citizens. Is it a "must" to register the company with SEC?
Yes. The operator of a similar platform
was subject to an SEC enforcement action because he failed to register with the SEC as a securities dealer.
If you don't want to register, you need to prohibit US customers, and you should probably implement some basic measures like IP geolocation bans to cover yourself legally.
2. What if this stock brokerage works with P2P crytocurrency merchants to allow clients to convert the crytocurrency into USDT, and use USDT to purchase stocks via custodian account? What will be the relevant legal concerns in this case?
It won't make a difference whether you use bitcoins, USDT, euros, or whatever. These requirements pertain to the service itself, not the type of collateral customers use.