Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

The following sentence is false. The preceding sentence is true.
Are these two sentences true or false?

Christina has four daughters, and each of her daughters has a brother. How many children does Christina have?

You need to cut a round cake into eight equal pieces with just 3 cuts. Can you do it?

Which statement is true out of the following?
One statement here is false.
Two statements here are false.
Three statements here are false.

Where do you go to learn how to make ice cream?

You need to complete the maze by entering from the entrance marked below in the figure near the yellow circle, bottom left and leaving from the exit point near the green circle, bottom middle.

Rule of Game: You can move only by exchanging green and yellow circles.

The answer I give is yes, but what I mean is no. What was the question?

The Judge knows that Alamgir was killed by his girlfriend Jasline, but the judge is unsure whether to punish her. Why?

Evil warlock dislikes dwarfs and therefore he selects four of them and buries them. The dwarfs are buried in the ground and they are in such a way that except for their heads, their body is inside the ground. The dwarfs cannot move their body and they can view only forward. They are all buried in a line, and amongst the four, one of the dwarfs is separated by a wall. All the dwarfs are in the same direction. The last dwarfs can see two heads of friends in the front and a wall. In the last second dwarf can see one head of his friend and a wall. The second dwarf can see only the wall. The dwarf can see nothing.
Warlock comprehends the situation and tells the dwarfs that he has placed hats on their heads. There are two blue hats and two red ones. In all four dwarfs, one of them has to say what colour hat he is wearing. If the dwarf says the correct colour of the hat, they will be left free. If the answer is wrong, then they will be dug inside the ground till the very end.

What will be the answer by the dwarf and how will they answer?