If by correct you mean grammatical, then both sentences are correct. The second utterance (When I met him yesterday, he told me: "I will give you your money tomorrow") reports your friend's exact words - indicated here by the speech marks (i.e. direct speech). The use of direct speech in the spoken reporting of what someone told you, however, is very unusual and needs to have the appropriate prosody to be easily interpreted.
The first utterance (When I met him yesterday, he told me, he will give me my money today) uses indirect / reported speech, which is far more common in spoken language than direct speech. When reporting what was said to them, speakers often backshift the tense of the verb, so that the words "I will give you the money" become: He said he would give me the money.
However, backshift is not mandatory. Very often speakers retain the tense of the verb if they believe that what was said to them still holds true. So, for example, if Friend A told me yesterday "I will give you the money tomorrow" and I see Friend B early in the morning of today (firmly believing that A will keep his promise), then I can say:
When I met him yesterday, he told me he will give me my money today.
Of course, if it is the end of the day, and the probability of getting your money back is now low, then you would use would:
When I met him yesterday, he told me he would give me my money today.
Note: if you are learning this grammar for an exam, you are probably better off sticking with the backshifted version, which some consider to be the default usage in such contexts.
will is about something that definitely will take place at some time in the future, whereas can is talking about the ability to do something.
We will change our plan - we will definitely do it
We can change our plan - we are able to do it.
When you put the how question word in front of it, it weakens the difference between the two, because the question is clearly about the method we will use, rather than whether it will happen / whether we are able to make it happen.
could and would are the past tense forms of can and will. If we use a past tense to talk about a future situation, this is called a backshift. A backshift is used to indicate that we are reporting what somebody else said, or that we are talking about a hypothetical situation.
Could we change our plan? - hypothetically, are we able to change our plan?
Would we change our plan? - hypothetically, would we consider changing our plan?
Note that, when we ask a question, we invert the subject and the auxiliary verb:
We could change our plan tomorrow. - statement
How could we change our plan tomorrow? - question
Best Answer
The question is very formal and polite. It is a complete sentence; it uses the subjunctive; and it asks if it "suits" you to have the meeting at the proposed time.
Your reply is very casual. It is a sentence fragment; it does not include a subject; its only verb is an auxiliary verb; it uses a very informal sense of "sure"; and it does not have an object.
Yes, you can respond this way. A native speaker would understand you. This answer is much less polite than the question.
If I read this dialog in an American novel, I would think that the author is juxtaposing two characters for comedic effect. The person asking the question is old-fashioned, and is either a school teacher, a servant, or rich. The person answering the question is making a point of acting like a "hick", and is either a "school boy", or is much richer than the environment in which he (or she) grew up.