Let's untangle this conundrum. First, according to Genesis, Adam and Eve were in the Garden of Eden on Earth. It says that God in some form walked in the garden and talked with Adam and Eve. People disagree about where Heaven is and how to define it. One definition is that Heaven is being in the presence of God. That would mean that when God walked among them, Eden became Heaven. That is not how most people read this passage. Adam and Eve therefore were not in Heaven.
Second, the temptation that snared first Eve and then Adam was initiated by a serpent. The serpent is presumed to be under the influence of an adversary of God, a being created by Him and called variously throughout the Bible by the names Satan, the devil, Lucifer, the accuser and the dragon.
How did this adversary, who was originally created to be good, become evil? We don't know the whole story. Isaiah 14 gives us hints.
You suggest that it would be a good idea to shut the doors to Heaven so Satan or other evil beings could not enter. Depending upon which view of the end times you accept (called eschatology), that may already have happened or may still be in the future. Satan is pictured in the Bible as being able to enter God's presence in the past. This is seen in Job chapters one and two, and Zechariah chapter three. At a later point, Satan is cast down from Heaven and can no more enter God's presence in Heaven. Jesus refers to this in Luke 10:18: I saw Satan fall like lightning from heaven. There are also references to Satan being cast down in the book of Revelation.
The Bible refers to a war in Heaven in Revelation 12, but after a certain point, all evil has been ejected from Heaven and only is found on Earth. Then in the end times, when Jesus comes a second time, all evil will be expelled from the Earth as well.
You ask if it was God's plan from the beginning for Adam and Eve to fall and be expelled from Eden. Different Christian denominations will give you different answers to this question. It is tied up in the sovereignty of God, his ability to see the future or not, whether he predestines people to do or not do certain things. However, we do know that Jesus is described in Revelation 13:8 as having been "slain from the creation of the world". That means that God was certain that at least some people would fall, and he began his plan to save them from the very beginning.
Another question of yours is where Satan exists. Satan is a spiritual being. I do not think that his position can be specified using cartesian coordinates in our material world. All we can know about him is that he is able to speak and be heard by people and project some physical manifestations. He is called the lord of the power of the air. He was able to cause a tornado to kill Job's children, so has some capacity to affect matter as well as mind.
Concerning the angel Gabriel, the Bible says little. There are many fables, apocryphal books (like the Book of Enoch) and recent inventions that go to great lengths to list many angels, their deeds and responsibilities, Gabriel among them. The only sure information we have about Gabriel is that he stands in the presence of God, appeared to the Prophet Daniel, and also to Zechariah (husband of Mary's cousin Elizabeth) and finally to Mary, the mother of Jesus. These latter two visits are in Luke 1.
In Colossians, Paul warns people not to spend time obsessing over angels:
18 Do not let anyone who delights in false humility and the worship of
angels disqualify you. Such a person also goes into great detail about
what they have seen; they are puffed up with idle notions by their
You also suggest that Adam's problem was that he was made from soil. Many heretical groups (and other religions) believe that matter is inherently evil, possibly even created by an inferior God in competition with the good spiritual God. This includes Marcionism, Gnosticism, Zoroastrianism, etc. All Orthodox Christian groups (Roman Catholic, Eastern Orthodox, most Protestant, etc.) believe that matter is not inherently evil, since God pronounced it "very good" in Genesis.