Replace the question mark with the correct number in the below-given picture?

I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?

Can you find out the next digit in the following series ?

0, 0, 1, 3, 2, 6, 3, 9, 4, 12, 5, ?

Find the next number in the following series:
6, 14, 26, 98, __?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

You have 10 balls with you. A friend of yours out of nowhere asks you to place those ten balls in five lines such that each of the lines has exactly 4 balls on them. He needs to check your intelligence. Prove him by doing the task.

Three people check into a hotel. They pay $60 for the rent of the room. After they check-in, the manager realize that the rent for the room is $55. So, he gives $5 to the bellboy and asks him to give it to them. The bellboy thinks that it will be difficult for the three people to share $5 among them and seeking the personal benefit, he pockets $2 and gives the remaining $3 to them.

Now, each person paid $20 and got back $1. In this manner, each of them paid just $19 which totals to the amount of $57. The bellboy has $2 with him and adding them, we get $59. So where is the remaining $1?

The below given figure comprises of a pattern through which you can determine the missing letter. Can you push your mind to find the pattern and add the missing letter?

Can you complete the sequence?

192, 021, 222, 324, 252, 627, 2__, 9__?

Paul's height is six feet, he's an assistant at a butcher's shop and wears size 9 shoes. What does he weigh?