Last I read, you can only have ONE chain per Battle Step and ONE chain per Damage Step durring the battle phase. I need to verify this please.

In addition, how many chains can be started by your opponent durring your phases? For instance, my oponent starts a chain in the End Phase of MY turn, the chain completely resolves, may my opponent (or myself) begin a new chain before the End Phase actually ends? (or any other phase)

You can have multiple chians, during both steps. (Damage Step has more ridged rules though)

Both you and your opponent can continue to create new chians untill both of you agree to pass and move to the next Phase/Step. This applies to all Phases/Steps.