Can you find a five letter word that is left with only two letters if one is removed?

Mr. Buttons was all set to go to the village of Buttonland to meet his friend. So, he packed his bags and left for the village at 5 in the morning. Upon travelling on a road for miles, he came across a point where the road diverged into two. He was confused on which road to take. He gazed around and he saw two owls sitting on a branch. He thought he could ask for directions for the village from the two owls. So he went to the tree. There he saw a sign which read, "One owl always lies, and one is always truthful. They both fly away if you ask them more than 1 question."
Mr. Buttons was caught in the dilemma of what to ask? And from which owl to ask, since he only had one question. What should Mr. Buttons ask?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

What is full of holes but still holds water?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

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?

A shepherd had 18 sheep, out of which, all but ten died.

Can you tell us how many sheep was he left with?

Which country gets ill every time?

Two-person want to cross a river. Only one boat is present on the riverside that can carry only one person at a time.

However, they still manage to cross the river. How is it possible?

There's a day, that comes around once a year.
To celebrate the man, you hold dear.
He gave you life, love and will pick you up if you fall.
When it comes to guys like him, He's the best of all.
Who is he?