It belongs to you, but other people use it more than you do. What is it?

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

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

What is next number in the pattern below:

131 517 192 123 ?

How many Watermelons are there in the below picture?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

It's a protector.
It sits on a bridge.
One individual can see directly through it, while others wonder what it hides.

What is it?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?

What can you catch but never throw?