First of all (and most important), congratulations on your engagement! Best wishes for a happy life, both as a spouse and as a teacher.
I'm guessing, both because of your engagement, and also by the nature of your question, that you're young, and a native speaker (so you "know" the "correct" answer) but a relative newbie as a teacher (because you're looking for "rules" to pin your answer on).
Maybe it's not quite that simple, and yet it really is simple indeed. One idea that might help you a lot is to realize that there might not be a rule for every point of English grammar. On the other hand, it might also help a lot to remember that there are two rather distinct kinds of grammatical rules. One kind consists of plain facts: "The plural of
wife is
wives (and not
wifes)." "Main verbs in statements with third-person singular subjects acquire an "-s" at the end." There is nothing for the student to understand with these kinds of rules...they simply need to be memorized and applied. (Of course, that doesn't mean that it's always easy for the students).
Other kinds of grammar rules are generative; that is, they are intended to simplify things for students by lessening the memorization load. It is intended for language users to understand something about how the language is put together, so that one doesn't have to memorize every possible sentence in English, but rather can, by understanding the "map" provided by certain observations about how English works (which we rather misleadingly call "rules", thereby unhelpfully lumping them together with the first kind), put together meaningful and understandable sentences on the fly, so to speak. It also helps to remember that English, in particular perhaps, is extremely flexible so that skilled users can bend some of the rules to good effect in getting a "special" nuance of meaning understood by other skilled users.
Let's look at your sentences individually. The first one is probably built upon the assumed understanding that "people who study hard pass their exams." But your example sentence presumably refers to people who may not be studying hard. These particular subjects are, so to speak, rather
remote (conceptually) from those who follow the straight-line path to academic success. If their behavior is thus remote, perhaps also will be their likelihood of success. So the sentence, rendered:
They would pass their exams if they studied hard.
...exhibits two moments of remoteness in the choice of word forms:
would (rather than
will, which lacks remoteness), and
studied (rather than
study, which likewise is not remote). These words are chosen precisely
because the idea to be conveyed is NOT the same as is understood in "
people who study hard pass exams." Be sure to note, here, that the sentence is perfectly acceptable if we change both of those words to their
immediate forms:
They will pass their exams if they study hard.
So it is the prior existence of the remote form "
studied" that necessitates the use of "
would" in the earlier part to make a sentence which is understandable. You can read it as, "
They would pass their exams (but they won't) if they studied hard (because they won't)." But let's not make a "rule" here when simple understanding of what is going on will suffice. To my knowledge, there is no rule which states that if you have a remote form early in a sentence, then all other parts of the sentence must be remote too.
Your second example sentence is just a matter of understanding the timing of events. At the moment the sentence is uttered, Peter has already left. And indeed, the speaker could say as much. But if he did, he would be pinning his temporal focus on the moment of speaking. However, "
When Jack arrived at the party," is presumably sometime before this speaker says the sentence, so use of
Present Perfect form is not kosher. Rather
Past Perfect is more appropriate in this case...because the temporal focus is in past time.
I've already said way too much, and I apologize for that, but somehow I felt your question deserved a somewhat complete answer. I hope I haven't bored you to death.
Regarding your last question, and in view of some of what I said above, I think I'll let you decide for yourself:
Can you say, "
Sandy and I are going sailing on the weekend."?
Can you say, "
The weather is supposed to improve at the weekend."?
Larry Latham
.
), but hopefully the concept of mixing time will be clearer. You might also try creating a similar dialogue with other types of mixed conditionals (past affects present, present affects past).