I've got the S4 red (I think) and only problem I've had with it is the remote can be a bit tempremental sometimes. Won't work inches from the bike...
I just keep pushing the button and it eventually sorts itself (probably an old battery, I've had it over 2 years and never changed it)
In terms of affecting the bike battery, it drained it over winter, when I didn't ride it for 5 months, but it'll start after 3 months not touching it
Although all this is pretty relative, I only found out a few months ago if you push the button to set the alarm, it sets the immobiliser and the alarm, if you let it set itself, it only sets the immobiliser... The alarm still goes off if you turn the key in the ignition though!
So in conclusion - Just the immobiliser lasts between 3-6 months on a 1/2 year old motorcycle battery
Also, the bike looks good, but you've been conned, looks like it's a gen 2 to me....