3rd grade math exam and fake eggs

My high school friend's son is going to third grade (yes he is 9 years old), in one of the best schools in Beijing. Not only you need to pay to get in this public school, you also need to know someone. If you don't bribe the teacher who is in charge of your class, when your kid has a fight with another kid, the other kid wins. But despite that, they get a superb education. He's in the Olympics math class (like American AP), and these are two of the 16 questions in his final exam. I can't solve them:
1) given a sequence of numbers in which ith is the sum of i-1 and i-2, and where first 2 numbers are 1 and 3 (which makes it different from fibonacci, where 1 & 1 are first two)
1, 3, 4, 7, 11, 18, ...
what is the remainder of the 40th number in the sequence when divided by 5?
2) consider the number whose digits are the sequence of the squares of the natural numbers:
1, 4, 9, 16, 25, ... --> 1491625...
what is the 100th digit of this number?

Also, some smart #%#@% want to make a profit at the cost of the health of others - they make fake eggs - they look real, except they are plaster. My college friend bought some eggs from Walmart (yes they have Walmart here) and at least one of them is fake. Walmart apologized and said this is only from one of the suppliers and it's not common, so they sent a whole case of eggs to her and asked her not to publicize it.

We are happy to retour Forbidden City at our own pace this time, with much less people.