Can you demonstrate that "Jesus" is a very old name mentioned by the writers of the New Testament?
The New Testament was originally written in Greek. The name for our Lord was spelled "Iesous" in Greek (using English letters). Four people in the New Testament are mentioned having this name: The Christ (Acts 2:36), the son of Eliezer (Luke 3:29), Justin's other name (Colossians 4:11), and Joshua from the Old Testament (Acts 7:45). The Greek spelling is a transliteration of the Hebrew word "Joshua" which means "salvation" in that language. Such is demonstrated by the Septuagint translation of the Old Testament and by Acts 7:45. The name of our Lord continued to be transliterated into other languages. In German, it is spelled "Jesus" because German uses the "j" for a "y" sound. Since English is derived in part from Germanic languages, the spelling was carried over. However, English pronounces the "j" as a guttural, thus our pronunciation is different from how it was pronounced in first century. Not that it makes much difference, the meaning remains the same.
The Greek spelling is a transliteration of the Hebrew word "Joshua" which means "salvation" in that language.
Being the "ah" ending connected with female idea of a name, Joshua must be female or something like that.
Yes, people have been transliterating names as long as there have been multiple languages. For example, the word "amen" is a Hebrew word that has been transliterated into multiple languages, including English. Most Old Testament character's names were transliterated when written in the New Testament.
The name "Joshua" (English spelling) comes from the Hebrew word עשוהי. The Masorectic vowel system did not alter the Hebrew words. Developed around 900 A.D., they added hinting marks above and below the text to give readers an idea as to how the word is pronounced. If you want to see "Joshua" spelled without the Masorectic markers, you simply look at a copy of the Dead Sea scrolls which were scribed around 200 B.C. In Acts 7:45, the name "Joshua" is transliterated into Greek as Ίησού.
A form of this same name is used for Jesus: Ίησούς (see Acts 1:1 for an example). The name for Joshua in Acts 7:45 is in the genitive dative vocative masculine form. The name for Jesus is in the nominative masculine form, but it is the same name. All dictionaries note that the Greek name "Jesus" is a transliteration of the Hebrew name "Joshua."
In German, this Greek word was transliterated as Jesus. (See Acts 1:1 in Luther's translation)
You are incorrect that the "ah" at the end of Joshua indicates feminine. An "ah" at times can change a masculine word into a feminine word, but not always. A "ah" at the end of this name indicates a reference to Yahweh. In this case, the literal translation of "Joshua" is "Yahweh saves." God Himself stated the translation of "Jesus" when He spoke through the angel: "And she will bring forth a Son, and you shall call His name JESUS, for He will save His people from their sins" (Matthew 1:21).