What is the safe current carrying capacity of these booster cables?
Don't worry too much about how much current they'll bear. Just remember NOT to jump off a car battery, it'll fry your regulator! If you really need to know its capacity, consider a cranking current of under 30amps.
can i leave the charger plugged in and charging battery constantly
Yes, this uses the same technology as an Optimate. The battery will be monitored and topped-up as and when required. I would assume that a desulphate facility is also employed to prevent degradation of the battery due to non-use.