Is it normal to lose your appeite when you have a cold?

Normal because it's not only your sense of smell which is obscured by a cold, but of course also your sense of taste.

Eat what you feel like eating and drink lots of water.

There's an old saying "Feed a fever, starve a cold" but some people say it the other way round, who knows? Colds don't usually last long enough for eating less for a while to be an issue, just stick to the chicken soup and whatever else you feel like eating.

Its ok.

yea

Yes. You still need to eat.
Appetite is the physical desire for food. If you are thirsty, you are already dehydrated. If you go without food long enough you can feel severe pain.
Your body will 'turn off' or limit activity of the digestive system when you are sick and/or injured. It's using most of its energy to fight (and build antibodies if sick) to whatever you have or heal from whatever injury.
What you eat and how much is a big factor. The 'fuel' (food/drink) you eat determines how well your body functions. Crap/junk food is like putting bad quality dirty fuel into a car. Do the opposite and it runs better.

Well, yeah...breathing is difficult, you may have swallowed a not small amount of mucous...hot, steaming soup will help with congestion, possibly help a sore throat, gets some fluids into you...

It won't cure you, but it may help ease some symptoms.

...now I want chicken soup. Haven't had that shit in years...even though I just got over a cold.