What does this below rebus puzzle mean?

A man is sitting in a bar when a rich man sits next to him. He turns to the rich man and says, “Did you know I know almost every song that has ever existed?”

The rich man laughs. The man then says, “I bet you all the money you have in your wallet that I can sing a genuine song with a lady’s name of your choice in it. The rich man laughs again and says, “OK, how about my daughter’s name, Jamie Armstrong-Miller?” Minutes later, the man collects his cash and the rich man goes home cashless. What song did the man sing?

Which city is three-fifths chick two third cat and 50% goat?

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

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?

Three brothers Jacob, John, and James live in Mexico City. The product of the ages of these brothers is 175. Jacob and John are twins. How old is James?

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?

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?

Can you make a fire with just a single stick?

An explorer goes on an exposition in the jungle. He sets up camp in the middle of the jungle. The next morning he sees something with a head and a tail, but he is not afraid. What did he see in his bag?