What is the argument and Biblical basis that it is possible to know God from nature? What is the Biblical basis for the argument that it is possible for someone to learn limited (non-salvific) information about God without learning about him from the Bible or another believer, such as from nature?
Well you have two questions here and there are opposite answers for each.
Can you know about God without the Bible or other believer? Yes according to the Bible you can.

Romans 1:20


  For since the creation of the world God's invisible qualities--his eternal power and divine nature--have been clearly seen, being understood from what has been made, so that men are without excuse.


Psalms 19:1-2


  1 The heavens declare the glory of God; 
     the skies proclaim the work of his hands. 
  2 Day after day they pour forth speech; 
     night after night they reveal knowledge. 


But then comes the title question. Is it possible to KNOW God from nature? The answer is no.   Just like you can learn some things about my intelligence by looking at the way I code programs, you could never KNOW me just by looking at my code. In fact you could get the wrong idea about me completely if you only look at the actual code and don't read the comments in it! You've got to come to where I am if you want to know me. That's just logic, but what does the Bible say about that? How would we 'come' to God? 

John 14:6


  Jesus answered, "I am the way and the truth and the life. No one comes to the Father except through me.


So you can know about God without help from the bible, but I don't think you can say you could KNOW God without either the Bible, or others who know Him, because in order to KNOW God you have to have faith in Jesus, and while the heavens openly and obviously declare the glory of God, they don't obviously announce the person of Jesus Christ.  However, that doesn't mean that if no Bible or christian is available you can't ever know Him, God said in several places those who seek Him will find Him.  For example:

Deuteronomy 4:29


  But if from there you seek the LORD your God, 
  you will find him if you look for him with all your heart 
  and with all your soul. 


But if there is scripture or other christians available and you don't consult them, how could you claim to be seeking God with all your heart and soul?