I have no idea what I'm talking about, but if you get lost, you can frame your argument in an analogy and build your way up from there. As long as your argument is rational, you can find parallel examples in almost any topic (especially topics you're deeply familiar with!). This kind of arguing doesn't rely on fact, but broad general concepts, which should give you a lot of leeway for where you want to take your discussion.

Practice should help; there are debate clubs for that. Or try debating politics - it's mostly useless, but you'll never lack willing opponents. Knowing your subject very well helps, too. Staying calm is always useful; I have no recommendation on how to achieve that, though (I never really had to work for that.)

I have seen many people have this issue. Being very smart and not being able to construct and argument on the feet. I always advise them to join Toastmasters. I'm a member and it has greatly improved my persuasive abilities.

The trick to speaking well is practice. Talk through your arguments in a safe calm environment, speak freeform without stopping, record and watch your practice sessions. If that sounds like too much work, try Toastmasters.

Better yet, have long conversations with people who speak well and with whom you resonate.

Expect to be challenged when conversing. When speaking, prepare your next point. Appear calmer and more confident than the other person. Relax.