In a Self-Directed Solo 401(k) with a trust or a Self-Directed IRA with an LLC you can open a brokerage account in the name of the retirement trust and trade public securities; however, you cannot have a margin account. You'll need to use the EIN of the Self-Directed Solo 401(k) trust or your LLC in an IRA instead of your SSN when you setup the brokerage account.
There are other institutions who specialize in these assets classes, however, most of them will not allow you to hold both standard and alternative assets. Using a Rocket Dollar account will help you maximize your diversification across your entire retirement portfolio.
You cannot short stocks. You can trade options, puts, and calls as long as they do not require a margin account. You can't trade naked puts and calls as this strategy would require a margin account.
Extensions of credit are a prohibited transaction. Here are some examples of prohibited transactions.