In this sentence, is this
疲れて explaining the reason? Why was he not able to study? Why can't we use
You could use ので or から, you just don't have to as it can be implied. Compare «I was tired yesterday and I couldn't study» vs «Because I was tired yesterday I couldn't study». Your example is essentially the former.
The いて is the te-form of いる which marks the verb as progressive or ongoing.
疲れる — To be tired
疲れている — Is tired
疲れていて — te-form of being tired