Problem-2: Why does the manufacturer mention two different values for
"Collector- Emitter Breakdown Voltage" and "Emitter-Collector
Because the transistor in the the opto-coupler is meant to primarily run with up to 100 volts on the collector with respect to the emitter. If you run it in reverse firstly you will get operational problems and secondly it can't be expected to survive a reverse voltage greater than 7 volts.
Problem-1: I cant figure out the gain of the photo-transistor (like in
other normal BJTs). There is something mentioned Current Transfer
Ratio which I guess has something to do with the gain of transistor.
Not sure though.
Remember that this device is an opto-coupler so it has an emitter (LED) and a receiver (photo-transistor) therefore, its main use is in opto-isolating and, for opto-isolation, the potential user is interested in how many mA you have to drive the LED with to how many mA you get on the transistor. This is called the current transfer ratio (CTR) and is quoted at between 100% and 300% at 10 mA. Figure 2 also tells you that if you operate with a slightly lower LED current (6 mA) you might get about 10% more CTR.
Although the device has a base connection and you might have thought that the data sheet would give hFE for the photo-transistor, it doesn't (and most of them don't). The only hint at what happens when you connect a resistor from base to emitter is shown in figure 4 so, if you can do the math and reverse things around, you might be able to eventually work out what the photo-transistor hFE is.