First, science will show it is impossible. You're looking for an explination which will satisfy the doubts.
Question: How can Santa have enough time to deliver toys to everyone?
Answer: First, let us adjust the scope. Santa only delivers toys to those children who celebrate Christmas. Many countries don't celebrate Christmas.See examples here. Second, Santa has a full 24 hours of darkness. Additionally, we know that time is not fixed. The passage of time is relative to speed and mass. Perhaps Santa's work takes weeks but is compressed from our frame of reference to one night.
Question: How can Santa answer all the children? Does he know all the languages in the world?
Answer: What most people don't realize is that Santa is a Hyperpolyglot. He has an uncanny ability to learn languages. There are documented cases of people speaking more than 50 languages. Since he so long lived, he has mastered many. For those he doesn't know, he has a cadre of Elvin translators to assist him. It is actually the Elves who construct the naughty and nice list for him, distilling the intelligence reports from all the Shelf-Elves and other informants (like the family pets and school administrators.) Once again, not every language group celebrates Christmas. While there are almost 7,000 languages, 94% of the world population speaks around 400 or fewer.
Question: How will Santa leave presents if there is no chimney?
Answer: Santa employes several techniques. First, he has a magic key. It operates like a skeleton key. He has also been known to use a window. Since the size of Santa seems to change (from tiny Elf in the night before Christmas to human-sized in every Department store), Santa may be able to alter his size to fit under doorjambs.
Question: How can Santa know where to deliver, if we are not at home, and instead at grandparents' house?
Answer: Because parents leave a note for Santa telling him where you are. It works like the postal services mail forwarding servcie.
Question: How can he eat all stuff that we offer him? (I don't know if it's the same everywhere, but we offer some food to Santa during the night, and in the morning, the food has disappeared.)
Answer: With time dilation, we don't know exactly how long it might take Santa to deliver all those presents. However, he does work very quickly and works up an appetite. Santa has been known to leave a cookie or two for dad or mom to eat if his belly was full at the time.