Krokodili (to crocodile) means to speak your own native language where Esperanto would be appropriate. There is also aligatori, (to alligator) which is to speak a language which is not your native language rather than Esperanto. There is also an overarching term, serpenti (to snake), which means people are both krokodilas and aligatoras.
E.g. An Englishman and a German both meet at an Esperanto conference and rather talk in Esperanto, they both use English instead. So they both would serpentas, but the English speaker would krokodilas and the German speaker would aligatoras.
I've never heard of serpenti for this before...
On the other hand, thinks such as kajmani and lacerti aren't realy fixed, either -- I think everyone agrees on what krokodili means and most people on aligatori but beyond that it can get rather vague.
For example, some make a distinction between "speaking a language which is neither Esperanto nor the native language of either speaker" and "speaking your listener's native language which is not your own native language nor Esperanto" while others lump both under aligatori.
According to the Esperanto Wikipedia-page on reptiliumi, gaviali seems to fit the bill:
Gaviali estas Esperanta idiotismo kun la signifo "paroli Esperanton, kiam alia lingvo pli taŭgus" aŭ kun la signifo "uzi Esperanton por ke ĉeestantaj ne-Esperantistoj ne komprenu nin".
To gaviali is "to speak Esperanto, when an other language would be more appropriate" (either because you just met another Esperantist, and despite being accompanied by other/-s who don't understand Esperanto, you switch to Esperanto, or because you and someone who understands Esperanto wants to say something that you hope no-one else will understand).
I think it's most often used derogatorily, yes - to reprimand people who speak non-Esperanto languages at Esperanto events.
On the one hand, many people come to such events to practise Esperanto, something they don't get the opportunity to do that often perhaps, and so want to spend as much time speaking and listening to Esperanto as possible; and they want to encourage new learners to speak and practise as much as they can.
But on the other hand, celebrating language diversity could mean allowing any language, not looking down on someone for choosing not to speak Esperanto.
My mnemonic is that accusative is when the subject accuses the [direct] object: La subjekto kulpigas la objekton.
The boy hits the ball. The cat catches the mouse. The soprano sings the song. Subject, verb, direct object.
In Esperanto, the subject always ends in -o, and the direct object ends in -on. La knabo frapas la pilkon. La kato kaptas la muson. La soprano kantas la kanton.
The exception is when the verb is "estas." That's because then the subject and the object are the same thing. The subject isn't doing anything to the object.
La kato estas tigro. Duo estas strigo.
Then there are fancier sentences: subject, verb, direct object, preposition, indirect object: The boy throws the ball to the dog. La knabo ĵetas la pilkon al la hundo.
The subject gets an -o. The direct object gets an -on. The indirect object (the noun with a preposition in front of it -- "to the dog", "al la hundo") gets an -o.
Accusative case is really quite simple. When a noun is the direct object of a verb, it is in the accusative case. This simply marks that it is being acted upon by the verb. "Mi donas pomon al vi" = "I gave an apple to you." Here pomo becomes pomon because it is the thing being acted upon by doni. Esperanto also uses the accusative case to mark the destination of a motion verb, although I'm not sure why. I think you can simply use "al" in such a case to circumvent the accusative.
The advantage of marking the accusative is that it frees up word order. This is why you can say e.g. "Al vi donas mi pomon," because the cases of mi and pomon are clearly marked.
You probably never visited the Dutch course! Over there, sentences like "Ik ben een banaan" (I am a banana) and "Jij bent een schildpad" (You are a turtle) abound, and that to me makes the course feel much lighter and fun. That said, that's precisely what the comment boards are for - for people to come stumble onto things and ask others for help and learning something through that process.
There are such sentences in different courses (maybe even in most/all of them). Although, I clearly remember only "Yo soy un pingüino." ("I am a penguin" in Spanish) and "Ho un coltello nello stivale." ("I have a knife in the boot" in Italian), I am pretty sure there were some similarly ridiculous ones in the German and French courses, too. :)