First of all, both "on time" and "in time" imply some sort of dead-line - a moment (usually pre-arranged) after which you would be late. They are quite different in what they apply to.
"on time" in English is a generalization most often if not always used by itself: "I arrive on time", which means I was not late. Late for what or on time for what has to be discovered from the context.
"in time" is always used with some sort of qualifier, most often "I arrived in time [to do something]". If there is no following verb, context almost always allows you to infer it.
For example, "I arrived in time for coffee" is a short-hand (see below for what "short-hand" means; it's very useful) way of saying, "I arrived in time to buy a cup of coffee" or "to get a cup of coffee from the kitchen" or "to get a cup of coffee before the conference started".
American English-speakers never say, "I arrived on time [to do something]", except where they have not learned proper grammar. Unfortunately, that can apply to a large number of us. You would be understood whichever one you used.
Short-hand (I'm mentioning this out of an abundance of caution) is a way of taking down dictation when someone is speaking. It looks like some kind of hieroglyphics. When we say something is "short-hand" for something else, we mean that it is a very minimal way of referring to something else which would take a lot more words.
For example, "To meet for coffee" is a short-hand way of saying, "to meet at a place that serves coffee and other beverages (and probably food, too) where we can sit down and have a discussion." You don't have to actually drink coffee.
"On time" refers to a scheduled or appointed time: arrivare in orario if a schedule, arrivare puntuale if an appointment or an agreed time.
"In time" refers to a period before the appointed time: arrivare in tempo. In time for dinner = in tempo per la cena; in time to eat = in tempo per mangiare; NB in plenty of time = in tempo utile.
So both should be allowed here, but I think "in time" looks like a slightly better translation in the context of "Ricordate ...".
there are many difference between "in time" and "on time"; there are some differences between "to arrive in time" and "to arrive on time" - but given the imperative command to "remember to arrive in time" the meaning is the same as "remember to arrive on time." (you can also add "remember to be on time", and if you ignore the task of attempting literal translation and just wanted to convey the same meaning - "Don't be late" ) This is one of the rare cases where duolingo is providing a context, sadly without understanding the context.
I'd say there is a difference. If you have made a previous commitment to a particular time with someone then you need to arrive ON time. If you have to be somewhere by a certain time that was decided without any prior agreement by you (e.g. the start of a movie, or departure of a flight) then you need to arrive IN time, perhaps because in these cases it is generally expected that you will arrive ahead of time. Where you have made an appointment with someone (e.g. a doctor or a friend) you only need to arrive ON time as far as they are concerned.
In time is more colloquial and informal. I even had to read some of the comments to be reminded of when "in time" was used!! If used, its present or near-present situation. Like "just in time" which means "barely made it" or "just got here". The above lesson should say "ON time" as "in time" would not exist in this statement as it's just plain BAD English.
For your own learning, just assume "ON time" until someone corrects you otherwise.
puntuale punctual . In orario on time (also used as "schedule") vs in ritardo "late"
pronto is prompt or "hello!" and presto is soon.
This sentence is a command (or when present or when future tense) in indep clause which means that the dep clause can be in the Present subjunctive : arrivi .
This sentence is using "di" followed by infinitive for remember , ricordare. Forms of Dimenticare also require "di" followed by an infinitive. Sperare, cercare, etc There is also a reference to the subject being the same in dep and indep clause can use the infinitive but when the subjects are different, the subjunctive is used.
Ricordate vs ricordati
I need help with this one. All the documentation I have found shows that the proper enclitic.(suffix attached to the end of a verb) for the reflexive pronoun of the second person singular is ti not te. A lookup in Garganzi gives that te can be a
forma complementare tonica del pronome personale tu, che si usa come complemento oggetto quando gli si vuol dare particolare rilievo e nei complementi retti da preposizione
forma complementare atona del pronome personale tu; si usa come complemento di termine al posto del pronome personale ti in combinazione con gli altri pronomi atoni lo, la, li, le e con ne
Therefore, according to Garganzi te in no way can be used as an enclitic. Theoretically, at least, because a Google search shows 25% more results of ricordate di than ricordati di. So I guess it cannot be a mistake on DL's part and the sentence is correct even though grammars seem to think otherwise. I am really flabbergasted and in need of advice. Thanks in advance for any hint on this matter.
You are confusing "translation" with "meaning". Your translation is clearly wrong, with a different verb and the negative. Your meaning is very similar, and yours is a common way to say it in English. I instinctively feel that it is not perfectly identical, but it would need a philosopher to explain why! Something about the underlying assumption about the listener.
Duolingo has to focus on translations. Otherwise there'd be chaos.
It is wrong. Ricordare di IT infinitivo is "remember EN infinitive" which includes "to ...".
What you've typed is actually a reference to a past action, not a future imperative. I can't imagine a context for "... arriving on time", but "do you remember picking up the knife?" has no doubt appeared in many a courtroom drama. It would probably be best translated by a past tense: perhaps "ti ricordi di aver raccolto il coltello?"
The movement category refers to the verb before a, not the one after it. Ricordare isn't movement.
You might find https://forum.duolingo.com/comment/2702088 helpful. You'll discover that there are no easy rules about prepositions - you just have to learn them as you meet them. (The same applies in English.)
You can meet ricordare di in the examples in https://dizionari.repubblica.it/Italiano-Inglese/R/ricordare.html.