Existence usually means "the state or fact of being", but there are many different views on the meaning of the word existence, and what it means to exist.
In English, existence is usually connected with the verb "to be".
The first sentence can be understood to say "I exist as a human", and simply speaking, this is probably true. The fourth sentence is more difficult to understand, because it can be understood to say "seven exists as the sum of four and three", but "seven" is not something that we can see or touch like a pen or a human.
The question "What is existence?" is a very important one for philosophers, and many people think Aristotle is the first human being to have thought seriously about the question.
A universe from nothing by Lawrence M. Krauss. Free Press 2012. The book discusses modern cosmogony and its implications for the debate about the existence of God. The main theme is how "we have discovered that all signs suggest a universe that could and plausibly did arise from a deeper nothing... by processes that do not require any external control or direction."[1][2]