It should have no problem starting at 11.4 volts, as when starter turning will drag it down to 8/9 volts anyway.
It does sound like you battery may be a little tired, get it RAPID DISCHARGE TESTED to see.
The alarm will certainly sap power, but should not be enough to prevent starting overnight unless battery u/s.
15 minutes idling will not put back in what you took out for starting car, it needs a good run or charge overnight.
tabetha