Taking a shower and the water suddenly turns cold? Now this I have heard of (from experience). Could be a number of things - pressure dropped in the equaliser (not sure of it's real name) inside the boiler. Water pressure not up to correct level, faulty thermostat etc.
Common theme - the boiler needs looking at.
As for the thermostat being at 75 degrees, well that must be the boiler and therefore water in the radiators temperature (Couldn't possibly be the room thermostat for glaringly obvious reasons). 75 should be ample for getting the house really warm, I think mine is set at about 60.
You won't really get hammered for the gas bill setting the boiler temp higher, as it will get the rooms warmer faster, and should then switch off, however it is more efficient to have the temperature lower, so that the boiler condenses at optimum level. These boilers at full whack run at about 24kw

but once it settles into a steady running, this will drop to about 7kw I'm told.
If your boiler though is only a year old, no way should this not be heating the house.
You really need it looked at.
I'm one to talk though, I sit under a duvet most nights with the heat off