Our product and our sum always give the same answer. Who are we?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

In a classic wine shop, the list of three most popular wines are:
- The cost of 1 French wine bottle: 500$
- The cost of 1 German wine bottle: 100$
- The cost of 20 Dutch wine bottles: 100$

John entered the wine shop and he needs to buy
- All three types of wine bottles.
- Needs to buy Dutch wine bottles in multiples of 20.
- Need to buy 100 wine bottles in total.

John has only 10000$. How many wine bottles of each type, John must buy?

An equation has been laid down using a few matchsticks. However, as you can see, the equation is not correct. Can you correct the equation if you are allowed to add or remove 5 matchsticks?

It walks on 4 when its young, walks on 2 when it's older, and walks on 3 when its very old?

I am a word of 12 alphabets.

* Alphabets 12, 4, 7, 2, 5 : Eastern beast of burden
* Alphabets 1, 8, 10, 9 are street made famous by Sinclair Lewis.
* Alphabets 11, 3, 6 are past.

On whole it means a person suffering from delusions of greatness.

What Is it ?

You bought me for dinner but never eat me. What am I?

What four weights can be used to balance from 1 to 30 pounds?

Which tank will fill first?

A wealthy man lives alone in a small cottage. Being partially handicapped he had everything delivered to his cottage. The mailman was delivering a letter one Thursday when he noticed that the front door was ajar. Through the opening he could see the man's body lying in a pool of dried blood. When a police officer arrived he surveyed the scene. On the porch were two bottles of warm milk, Monday's newspaper, a catalog, flyers, and unopened mail. The police officer suspects it was foul play. Who does he suspect and why?