Looks like the Billing kit, rather than the Artesania Tug.
Scale, measure the height of the stanchions, probably safe to assume that the real ones would be 1 metre high, get the scale from that. A googled picture shows something very similar with "35" in its title. If that indicates a 35 foot boat, and if the model is about 35 inches long, that gives 1:12.
Bigger amp battery – yes, but ditch SLA, go for a different technology. SLA are good ballast, using a getter battery will increase both boat speed and run time. NiMH will give more capacity for the same weight and can be got at the same voltage. LiPo will give a lot more capacity for the same weight (more volts as well – a 2S Lpo gives 7.4 volts), but at the cost of needing more careful handling.
Not being able to see exactly what motors are there, it's hard to suggest an alternative that would be an improvement.
ESC. Good or cheap. A choice is needed. If just one for a pair of 540s I would go for a Viper Marine 40. Not the cheapest, but you only need to buy it once. Dumping and unsatifactory cheapo and then buying the right one does cost more. without knowing the motors involved, thats guesswork anyway.