Question 1
Both statements are correct, though they have different emphasis. When you say:
Please! Call me.
You're simply asking someone to call you. If you add "do", making it:
Please! Do call me.
Then, there's an implication that the other person may not call -- they may be forgetful or unwilling -- and you're emphasizing that you want them to make sure they call you.
Question 2
I speak American English, so I'm going to substitute "will" for "shall", since it's more common in American English. All the following statements are correct and have essentially the same meaning:
Yes.
Yes, I will.
Yes, I'll call.
The three answers may vary slightly in terms of formality, but it's not a significant difference (shorter answers and answers with contractions are ever so slightly less formal).
Question 3
Only the first sentence is correct:
Does he do all those things?
When constructing a sentence starting with "Does he/she...", you use the base form of the infinitive (e.g. "to do" -> "do").
"Let me know when you get here" is the most common way to express this idea. "Let me know when you are here" is also fine. "Let me know when you come here" is weird, since the process of coming from there to here takes some time, but "let me know when" is discrete.
By the way, at least in the US, abbreviating "you" as "u" is often seen as a little childish. I would never do it unless I was paying by the character (like on a telegram or something!)
Best Answer
You cannot use "do" as a question word with "is". "Do" means to act. The word "do" is used in questions to ask whether the action is being performed or not. While "is" is a verb, it does not describe an action.
To form a question with "is", start with the statement:
Now instead of adding "does" as a question word, move "is" to the beginning: