Do Protestants understand Jesus to be both "the son of Adam" and "the son of God"? Do Protestants understand Jesus to be both "the son of Adam" and "the son of God"?
Protestants believe that Mary was a virgin when she conceived by the power of the Holy Spirit, but they do not go along with the Catholic view that Mary herself was without sin.  The Bible says nothing about Mary being sinless. 

The Protestant view is that Jesus was fully human and this came from Mary being his biological mother. Jesus alone was born of a virgin, conceived by the Holy Spirit. Jesus had no human father. The fact that Jesus was without sin is clearly stated in the Bible:


  For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God (2 Corinthians 5:21).
  
  You know that he appeared in order to take away sins, and in him there is no sin (1 John 3:5).


I am unfamiliar with the expression that Jesus was “in Adam” but the Bible likens Jesus to the first man Adam:


  The first man Adam became a living being; the last Adam, a life-giving spirit. The spiritual did not come first, but the natural, and after that the spiritual. The first man was of the dust of the earth, the second man from heaven. As was the earthly man, so are those who are of the earth; and as is the man from heaven, so also are those who are of heaven. And just as we have borne the likeness of the earthly man, so shall we bear the likeness of the man from heaven (1 Corinthians 15:45-49).
  
  Just as Adam was the first of the human race, so Christ is the first of those who will be raised from the dead to eternal life.  Adam came first on this earth and was made from the dust of the earth. While it is true that Christ has existed from eternity past, He is here called the second man or second Adam because He came from heaven to earth many years after Adam. Christ came as a human baby with a body like all other humans, but He did not originate from the dust of the earth as had Adam. He “came from heaven.”  Source: https://www.gotquestions.org/Jesus-second-Adam.html


That, as far as I am aware, is the Protestant view of Jesus being both fully human and fully God.  Mary was a descendant of Adam and, like all humans, was herself subjected to inherited sin.  Jesus was without sin because he came from heaven, from above, and no human father was involved.

Additional information regarding the Baptist view of Jesus being without sin:


  The Baptist Confession of Faith (1689)  Section 8: Christ the Mediator
  The Son of God, the second person in the Holy Trinity, being true and eternal God, the brightness of the Father's glory, of the same substance and equal with Him;
  
  
  Who made the world, and who upholds and governs all things which He has made,
  did, when the fullness of time had come, take upon Himself man's nature, with all its essential properties and common infirmities, with the exception of sin.
  He was conceived by the Holy Spirit in the womb of the Virgin Mary, the Holy Spirit coming down upon her and the power of the Most High overshadowing her, so that He was born to a woman from the tribe of Judah, a descendant of Abraham and David, in accordance with the Scriptures.
  Thus two whole, perfect and distinct natures were inseparably joined together in one person, without conversion, composition, or confusion;
  So that the Lord Jesus Christ is truly God and truly man, yet He is one Christ, the only Mediator between God and man.
  http://www.romans45.org/creeds/bcof.htm#part8
  


The New Testament writers had to combat a form of Gnostic teaching that denied the full humanity of Christ.  They believed flesh was evil but spirit was pure, therefore God would never have incarnated as a fleshly human.  They said Christ only appeared to be human, but it was an illusion – he was actually spirit.  The New Testament declares Jesus was human and also God incarnate.