How to turn on a optoisolator with a desired resistance
You cannot change the characteristics of the transistor inside the optoisolator.  If you need to switch more current than it can handle (and you need the isolation that the opto provides), then you will have to use the opto to drive a larger transistor that can switch the load you have.  

Measuring the "resistance" of a transistor C/E junction is not meaningful.  

That part of your question, as posed, cannot be answered.

As to the second part -- if you want to switch a relay with the output of the comparator using a small NPN transistor is a fine choice.  

Consider that you are going to want to use active-high output from the comparator in that case, so you will need to reverse the sense of the inverting and non-inverting inputs to the comparator.  Simply drive the base of the BC547 through a suitable current-limiting resistor.  Keep in mind - the maximum collector current is rated at 100 mA - just like with the photocoupler above, you're going to be limited how large a load you can switch with such a small device.