HDMI to VGA does work if you have the pass-through technology if your hypothetical television accepts, but that is most of the time available on pretty costly equipment.
As it stands, television companies are in the business of omitting passthrough technology and just giving you separate...
No doubt it is the old part of the house that is taking its toll on the projector, as what frost has said, you need an electrician to fix the wiring of the room. :/
There's interference because of the old material that is not good at shielding the electric current.
What you can do, is get an...