what does this picture(rebus) riddle means ?

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

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

How many runs at maximum can a batsman score in a normal one-day match? Consider the fact that the conditions are ideal and there are no No Balls, no Wide Balls and no Extras in that match.

Count the number of balls in picture below:

What goes through cities and fields, but never moves?

What does man love more than life, and hate more than death or mortal strife; that which satisfied men want; the poor have, and the rich require; the miser spends, the spendthrift saves, and all men carry to their graves?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?