What does the below rebus riddle means?

Anabelle is a clever trader of rare artefacts. Each day she carries three boxes each filled with thirty artifacts. The boxes can't hold more than that. She travels far in northern lands to sell these artefacts but on the way, she comes across thirty checkpoints where she has to shed one of the artefacts for each sack to the authorities for letting her pass.

How many artifacts will be left with her when she reaches her destination crossing all the checkpoints?

Astrology starts with the alphabet A, Biology starts with B, Psychology with P and Limnology with L.

Can you find an "ology" that begins with a P?

Can you find the next number in the below sequence
3 , 7 , 10 , 11 , 12 , 17 ?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

I have a head like a cat and feet like a cat, but I am not a cat. What am I?

A journalist was investigating a sacred cult in the jungles of Africa when he was caught by one of the person. He was confined in a cave till the leader arrived. The leader told him that he need to tell him a statement. If he thinks the statement is true, then the journalist head will be chopped off. If he thinks that the statement is false, his head will be smashed with a hammer.

What statement did the journalist make to survive?

Take away the whole and some still remain. What is it?

If eleven plus two equals one, what does nine plus five equal?

I am lying and I always lie. Tell me whether I am lying or telling the truth.