If EELS + MARK + BEST + WARY = EASY

What does HELP + BARK + WARD + LEAD equal?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

One day Jenifer meets the Lion and the Tiger in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays, and Wednesdays, and tells the truth on the other days of the week. The Tiger, on the other hand, lies on Thursdays, Fridays, and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Jenifer:

Lion: Yesterday was one of my lying days.

Tiger: Yesterday was one of my lying days too.

What day is it?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

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.

Can you write down eight eights so that they add up to one thousand?

Different lights make me strange by changing me into different sizes. What am I?

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?

There are two words one resembles the "state of rest" and the other is related to "writing/reading material".

Can you name these two words which also sound similar?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?