1) Honestly speaking in more than 80% we use perfective imperative. When we want somebody to do something immediately we use impefective. You also could check yourself with the following: in the first example the RESULT is important for us (The mother will get a vase and she will be happy) - so we use perfective. In the second example it's important how carefully we will be looking at the words we need to study - so we use imperfective to describe the process. 2) We use НА + Acc. when we'd like to say that we have only 5 minutes to have or do something. After this period of time we should give back or stop doing this one. Сестра взяла мою книгу на 5 минут. Через 5 минут она вернет мне мою книгу. 3) Both Кто там пришел? and Кто туда пришел? are correct. But there is a difference between them. When we wonder who comes to OUR place we ask in the first way. And if we speak about other place|direction we use the second one. Тук-Тук! (Knock-knock!) - Кто там? - Мама, это я. Маша, к тебе пришли. - Кто там ко мне пришел? Маша, ты была вчера на вечеринке? Кто еще туда пришел? I really hope that I could explain well :) Don't hesitate to ask me more details, I will be glad to help you.

3) сестра взяла мою книгу на 5 минут. why they choose на 5 минут and not За 5 минут? If you use "за", the meaning is "It took my sister five minutes to take my book", or something like this. BUT "на 5 минут" means a time-limit: "my sister borrowed my book for five minutes". More examples: Выйдем НА 10 минут? = Shall we go outside for 10 minutes? (But we will be back ten minutes later). Выйдем ЗА 10 минут. = It will take us ten minutes to get out.