We don't say "having a fever". We might say, "I have a fever," or as you said, "I am suffering from (a) fever." I'm honestly not sure if you could say it without the "a". "I'm suffering from fever" may be correct, but it sounds strange and old-fashioned to me, like something out of a very old novel. As for your other example, "I have a car," is natural. But I don't see the relationship. I have a car. I have a fever. Both are natural We would use the present progressive "am having" in a few situations, such as, "I am having trouble with this problem (in school)."

You wouldn't say "I am having a fever" because you have one already. The problem is better understood with the phrase "having a baby". When a woman is pregnant, she goes to the hospital when the time arrives in order to give birth. While that process is occurring, she is "having a baby". It describes the transition from "she doesn't have" to "she does have". That is what "having" means; it is creation. Here's another example. If you are enjoying yourself with your friends, you can say "we are having fun". That's because "fun" is not like "fever". Either you have a fever or you don't. The same is not true with "fun". "Fun" is something you are constantly creating so it makes sense to talk about "having fun". Likewise with a car. Either you have a car or you don't. However, you could special order a car custom built for you just the way you want it. In that case, while the factory is building your new car, you could say "I am having a car built for myself".

'I am having a fever' isn't said. These senses of 'have' (have a cold, have a car, have blue eyes) are stative verbs. Stative verbs are not used in the continuous form. 'I have a fever' is correct.

Both sentences convey the same meaning that the person is unable to play due to their fever. However, "suffering from fever" is a more formal and medically correct way of expressing it, while "having fever" is a more informal way of saying it. In general, it is recommended to use "suffering from" or "experiencing" when referring to medical conditions, while "having" can be used more casually in everyday conversation. Regarding your comment about "having a car" sounding natural while "having a fever" doesn't, this is likely because "having a car" is a common and familiar expression, while "having a fever" is not used as frequently in everyday conversation.