What has 13 hearts but no other organs?

What does this rebus riddle mean?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

Two men are in a desert. They both have packs on. One of the guys is dead. The guy alive has his pack open, and the guy who is dead has his pack closed. What is in the pack?

A swan sits at the center of a perfectly circular lake. At an edge of the lake stands a ravenous monster waiting to devour the swan. The monster can not enter the water, but it will run around the circumference of the lake to try to catch the swan as soon as it reaches the shore. The monster moves at 4 times the speed of the swan, and it will always move in the direction along the shore that brings it closer to the swan the quickest. Both the swan and the the monster can change directions in an instant.
The swan knows that if it can reach the lake's shore without the monster right on top of it, it can instantly escape into the surrounding forest.

How can the swan successfully escape?

Sally lives in a place where six months of the year is mild summer and the temperature drops significantly the other six months. She owns a lake where there is a small island. She wants to build a house on the island and needs to get materials there. She doesn’t have a boat, plane, or anything to transport them to the island. How does Sally solve this problem?

What does this rebus puzzle means ?

There was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?