The answer to your second question is that the sentence is just fine as it stands. “When will you be here?” and “What time will you be here?” are perfectly equivalent in all registers. The extra at sounds overly verbose and cumbersome. I would not call it “wrong”, but neither would — well, or should — anyone mark wrong a sentence without it.
The answer to your first question depends on who is doing the questioning and who is doing the answering. I am pretty sure at the fourth-grade level, they are not attempting to teach inflectional morphology. Rather, they just want to know whether the student can tell the difference between a sentence that refers to past events, to present events, or to future events. This is the only distinction that matters for a fourth grader (and arguably, for 99.9998% of the rest of the populace as well). What terminology they use is really not important.
They are asking at what time the parents will be able to meet with them on Tuesday. In that, it is asking about a time in the future, as the use of Tuesday clearly gives away. Therefore, I am sure that is the answer they want to hear. They are not asking about events in the past. They are not asking about events in the present. That leaves only one possibility, and that is in the future.
So that is the answer, and the fourth graders can go home now.
That is because the only super-ultra-fussy-correct answer is one that will do your daughter no good whatsoever, for it will in all likelihood be adjudged the wrong answer by her teacher:
The word can is a present tense modal auxiliary (one whose past tense form is could) which is here used to express time in the future, something that has not yet come to pass.
The word meet is a bare infinitive, and as such has no tense at all. that’s because only finite verb forms can have tenses, not non-finite ones. Although meet looks just the same as the unmarked present tense, this use of meet should not be thought of as being in the present tense. It is not. It is not in any tense at all. It is a bare infinitive.
Because the modal can is already in use for “to be able to”, we cannot then apply the more typical future-indicating modal of will atop what it is already there, since double modals are forbidden in Standard English (and will can sounds wrong in any version I am familiar with). So it has to stand for the future even though it is a present tense form. This is no longer true with “will be able to”, which is why I rephrased it that way.
Of course, one can also express the future via the present tense alone, as in “When are you able to meet with us on Tuesday?” But if I asked a fourth-grader whether that entire question was asking about the past, about the present time, or about a future time, I would mark it wrong if they gave me any answer other than future. Because in fact, it would be wrong to give any other answer to that question.
These are fourth graders, please remember!
English is perfectly capable of expressing actions in the past, the present, and the future. That is all that is being asked here. For the viewpoint of a professional linguist on this and related matters, please see this answer.
Here is the OED’s definition of the word tense:
Gram. Any one of the different forms or modifications (or word-groups) in the conjugation of a verb which indicate the different times (past, present, or future) at which the action or state denoted by it is viewed as happening or existing, and also (by extension) the different nature of such action or state, as continuing (imperfect) or completed (perfect); also abstr. that quality of a verb which depends on the expression of such differences.
Notice what they say about “or word-groups”. A tense can be expressed by word groups. So when I say I will be able to meet you on Tuesday, I am using the word group “will be” to express time in the future. That therefore is a use of future tense by the “or word-groups” definition given above in the OED.
Now, morphologically speaking, there actually is something else going on here, but that is not going to be the sort of answer to feed a fourth-grader. You will just confuse her and annoy her teacher, and possibly the other way around as well, if you make that attempt.
Best Answer
The use of would in the first sentence is grammatical, but it isn’t a future tense, and in speech it would normally occur as I’d. (The use of plying is a little strange. The normal colloquial word would be running.)