Solution:

142857

Explanation:
142857 * 1 = 142857
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142

Note: Such numbers are called cyclic numbers.

Solution:

a) Immediately

Explanation:
"Temperature difference" is the driving force for the heat transfer.
Since the coffee is initially very hot and hence it will be cool down at a very fast rate.
If we add cream immediately : The temperature will initially go down for sure but then will cool down at the slower rate as coffees mixed with cream is cooler than coffee alone and therefore heat cool down rate is less. Also, the cream will increase the mass of the content in the cup and hence larger mass will take more time to cool down.
Hence cream should be added immediately

Solution:

11

Explanation:
We are looking at the numbers in the form of 5k +1 or 5k + 3
i.e The number ends in 1 or 3
If we jot down all such numbers, there are 16 in total:
1, 3, 11, 13, 21, 23, 31, 33, 41, 43, 51, 53, 61, 63, 71 and 73

Now, let us remove the ones that are not prime and we have the answer as:
3, 11, 13, 23, 31, 41, 43, 53, 61, 71 and 73

Solution:

If we remove the first letter of the word and place it in the end. It will be read the same from front and back.

Solution:

A Spider

Solution:

Notable
Not-able, &
No-table.

Complete Sentence:
A notable Surgeon was not able to perform surgery on a lady as there was no table.

Solution:

20

Explanation :
The sequence is given in the puzzle is :
11 15 19 12 16 ? 13 17 21 14 18 22

Let's break the given series as below:
11 15 19
12 16 ?
13 17 21
14 18 22

Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 20.

Solution:

Check the image for the solution.

Solution:

In the attached picture, you can see that the formation allows 2 castles to be protected by the walls. Congrats!

Solution:

It's in the beer mug