Why is the hot water in the shower and lavatory running so slowly. The cold is fine and the outside faucet is fine.

Is the hot water running OK in rest of the house ?

No it isn't. The kitchen in the same way

Ok, source of hot water is at the hot water heater. Go the heater and do visual observation of the heater. Look for closed valves, leaks, or any abnormality. Also, if you live in cold weather, and your heater is in the basement, or outside structure, it may be possible that your heater has frozen incoming cold water line.