Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

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?

What building has the most stories?

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.

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

I am a five-letter word and people eat me. If you remove the first letter I become an energy form. If you remove the first two letters, I am needed to live. Scramble the last three letters and I am a drink. What word am I?

What's the next in the series?

H, Be, F, S, Mn, Kr, In, Gd, Tl, ?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

In my garden, I have many trees but only one of them is the mango tree. In these mango trees, there are some mangoes(as expected).

But after a strong wind, there are neither mangoes on the tree nor on the ground. Explain?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?