Hi, I have a brand new hot water heater and have never run out of hot water. If I so much as crack the sink with Luke warm water the shower goes cold. As soon as the sink is shut the hot water returns. Same for any sink, the other shower or the dishwasher. Is there a problem with my mix? The got water is currently set up to be blistering hot when not mixed with cold at the faucet. I have never messed with plumbing before and am very clueless. Thanks in advance for any help!

Start by turning the temperature on the heater down. By having it up high, you're using a low percentage of hot vs cold at the shower and any pressure drop in the hot supply(turning on the sink) will have a greater effect on the shower temperature. Pressure balanced shower control valves compensate for pressure changes and automatically lower the volume of the other fixture water supply to maintain the ratio/temperature.

The key words may be "brand new water heater". There are ways it could have been installed which could cause those symptoms, but we would have to be there or maybe see a picture of the installation to see what the problem is. My initial reaction is that the installer left out a check valve.