What are some scholarly biblical arguments for theistic evolution? As I have done my research on theistic evolution, which is the theory that God created the earth and everything in it but let the process of evolution happen on its own. 

Definition of Evolution: 
The process by which different kinds of living organisms are thought to have developed and diversified from earlier forms during the history of the earth.

My main question though is what evidence is there to support the variety of different claims that theistic evolution makes?
First of all, evidence for the claims of evolution theory, theistic or not, comes from observations. Therefore, I understand the question as asking for exegetical evidence that the narrative of Genesis ch. 1 is compatible with evolution theory.

That compability comes from the distinct usage of two verbs in Gen ch. 1 for the divine activity: bara (Strong 1254), "create", and asah (Strong 6213), "make". Bara indicates the exclusively divine action of creating something which is not the result of reshaping a preexisting entity, and is used, as bārā or wayyiḇrā, in:


1:1 &amp; 2:3 for the whole universe;
1:21 for the sea animals, the first living beings from the viewpoint of the Hebrews (for whom plants did not count as such);
1:27 (&amp; Deut 4:32) for man.


Thus, while sea animals were "created", meaning that their being did not come from mere reshaping of preexistent inanimate matter (since for the Hebrews plants did not count as living beings), birds and land animals were "made", meaning that their being came through the reshaping of sea animals (which BTW was just the actual case according to contemporary natural science), just as the sun, the moon and the stars were "made".

Man, in turn, was also "created", meaning that his being (i.e. his spiritual soul) did not come through the reshaping of an existing animal.