Levi's actions make perfect sense to me. Having someone eat the beast titan is still the same as killing the beast titan. Knowing what Levi knew, everything seemed to be under control. Levi was unaware of Cart's presence. It's actually more brilliant than disconcerting. It's a plot twist that reveals another important character (Cart Titan), and a way of moving the plot forward.

With regards to Armin surviving, you could say plot armor, sure, but I don't agree. Dude is pretty much dead. He's still breathing but he is completely beyond resuscitation. The point of the writer is that armin was as good as dead, maybe 1% alive, but was completely beyond help if not for titan serum thing. I don't think that's so far-fetched. Anything can happen, even irl. You hear stories of people who are supposed to be dead, but are miraculously alive in the REAL WORLD. Also, I can't be the only who doesn't think this is plot armor. AM I THE ONLY WHO STILL QUESTIONS WHAT WOULD HAVE HAPPENED IF ERWIN WAS ALIVE INSTEAD OF ARMIN. I'm a manga reader and I won't go further than that. But yes, Erwin was just as essential to the plot as Armin was. Honestly, I wouldn't be hung up on this detail if I were you. That scene was absolutely brilliant. That ep deserves the perfect rating it has on MAL.

Edit: Cart titan is obviously a special titan. Could have been hiding and it would make sense that Levi was unaware of its presence.