1. '-(으)ㄹ 지 모르다‘ is a ending pattern of verbs/adjectives(Grammar) It is used when the speaker cannot decide to do something to be sure of something. It is equivalent to saying " I don't know whether/if ……" in English.

Im a beginner so take my corrections with a grain of salt. 1. 그녀가 언제 올 거는지 몰라요. Would be thne correct way to say that, whenever a uncertainly clause is used, 는지 is used instead of what you said. 2. I think 드리다 needs to be used instead of 주시다 in this case? 3. B is correct because you are saying youre doing that thing EVERYDAY, therefore 는 is used. It doesnt make sense to use 한 in this case

Q1. As the sentence contains an interrogative '언제', you should change '것을' for '지를'. (To be exact, unlike '것' or 'when', '지' is not a pronoun. So you have to write 올 and 지 with no space, and Using '를' is just optional. But even Korean people are often confused about spacing '지', you just ignore it...) Additionally, '지' is used when you are not sure of something. So, in addition to using it with an interrogative, you can say 'I don't know if she comes or not' like '그녀가 올지 말지 몰라요' Q2. Although '주시다' is the right honorific form of '주다', but only when it is used to honor the subject. So you can use '주셨어요' only in the situation where 'the grandfather' gave you a present. When it means I gave 'my grandfather' a present, the right answer is '드렸어요'(the original word is 드리다), which is the completely different word that is only used to honor the object. Q3. If there is not any other context, b) is the answer because '지루해요' is the present tense. c) can't be the answer, because it means the tasks you are already done with and won't any more, so it can't make you bored now. d) is future tense, so it can't be the answer. But actually a), it sounds similar to c) though, can be the answer with other sentences. e.g. 'Now I feel bored with the same tasks I've done everyday, so from now on, I want to do other things'. I think it's because a) means the tasks you've done everyday, but it does not tell anything about the future

Q1. "그녀가 언제 올 것을 몰라요" is wrong because 것 is not used for this kind of a question. Questions involving "when", "what", "whether" and other wh- words and "how" are expressed with -지. 것 creates a noun clause similar to "that" in English. - 그녀가 언제 올지(를) 몰라요 (를 is optional and is usually dropped) = I don't know when she will come. - 나는 그녀가 올 *것*을 안다 = I know *that* she will come. Q2. 저는 저의 할아버지께 선물을 주셨어요 => 저는 저의 할아버지께 선물을 드렸어요. 주셨어요 is the past form of 주시다, which raises the doer/giver. Since 저 is the doer, the sentence raises the younger person instead of 할아버지. 드리다 is the word which has the same meaning but raises the receiver. There are a handful of words like this: 데리고 가다 / 모시고 가다, 인사를 하다 / 인사를 드리다, 말하다 / 말씀드리다, 물어보다 / 여쭈어보다, etc. Q3. 제가 매일 하는 똑같은 일은 너무 지루해요 a) 던 - 하던 means it happened repeatedly in the past, so it doesn't fit the present tense 지루해요. b) 는 - correct because -는 is a present tense form which can describe a one-time or repeated action. c) ㄴ (한) - 한 indicates one-time action in the past (or present perfect), so it contradicts 매일 하는. d) ㄹ (할) - 할 indicates a future action. You can't say something you haven't done yet is tedious.