Legal Question in Business Law in California

If by "trading account" you mean an account with a stockbroker firm where you can buy and sell securities such as stocks, bonds, commodities, options, etc. (financial trading), you would have to ask the particular firm (Merrill Lynch, Ameritrade, etc.) with which you wanted to do business. I don't think your immigration status would be a factor.

I'm also unsure what you mean by "corporate account" in your question. Individuals usually open individual accounts, where they trade securities for their personal gain or loss. I would think that in order to open a corporate account, you would have to show the broker firm proof that you were an authorized officer of the corporation in which name you wanted the account.

Finally, what do you mean by "sign off" expenses? This doesn't seem to bear any relationship to buying and selling securities, if that's what you mean by trading. Sounds like you are asking for income-tax advice. If you are earning or about to earn enough income to have need for writing off education, etc. expenses, you will have enough money to pay a tax advisor for personalized planning advice.