Closed loop gain is a concept in current to current or voltage to voltage amplifiers. I'm not quite sure how to define it in a current to voltage amplifier. I am however quite sure that open loop gain is GBW divided by frequency. Although not always and not at every frequency - check your opamp's datasheet for exact OLG vs freq plot. Note that OLG may vary a few dB from sample to sample.
OLG is defined as output swing divided by differential input swing. So it determines precision - higher OLG means that the inverting input is held closer to ground for the same output swing. You do the math.
There is no direct connection between OLG and TI except for one: for the same input current, higher TI produces higher output swing and therefore higher input swing. However, the same effect can be caused by higher input current, regardless of TI gain.
Note that when the inverting input moves away from ground, voltage across the feedback resistor changes and TI gain is no longer what you expect.