Color temperature in cameras is most easily described like this.
Set the camera to 5600k and take a photo with natural light, the photo will look natural.
Set the camera to 2800k and take a photo with natural light, the photo will look blue.
Set the camera to 10000k and take a photo with natural light, the photo will look orange.
So if you have a candle on the table that you want to look warm and candle color, your other lighting needs to be a higher
color temperature, say 5600k and set your camera at 5600k.
If you want your candle to have the same
color temperature as the lighting in the room, your other lighting needs to be a lower
color temperature, say 2800k and set your camera to 2800k.
So it's not about being bad mixing
tungsten and sunlight and
HMI, it's just that you have to realize your camera needs to be set to a single
color temperature and you have to decide what that is.
If you set your camera for
tungsten light, a high
color temperature HMI or
LED fixture will appear blue on film. If that's what you're looking for, great. If not, well, you need to match your color temperatures.
In your test
image with the pirate looking guy, the sunlight appears cool compared to the warm
incandescent desk lamp. Assuming that's your goal, you need to match your lighting color temperatures to that in your test.
On the front of your set, it looks great! Very good
build and attention to detail. I don't think anything will make it seem like a ship except
props. Get a
compass and some nautical looking charts or barometers to hang on the wall.
Props like you have on the
desk, help make it looked lived in. Just be careful to not use
props that wouldn't make it through a rough ocean voyage because they're too fragile or slide easily.